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They have the same exact goal they are offering to potential funders, protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

First, they care about the result. Not the philosophy.

Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that it is surprisingly difficult for them to do so. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with expertise on those practical details. So being favoured approach would mean extra funding and not favoured would mean reduced funding. Making a yes or no policy decision should be avoided.

Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.

Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.

EDIT:

From the long discussion in the comments because I probably should have mentioned this...

The thing is which of the reasons is most important depends on the person. It depends on which way you are looking at it at the moment. The others are then complementary to that. Different people in the same government will see it differently. Different people evaluating the same decision will see it differently. Same person looking at it in different context will see it differently. I specifically do not want to make this decision in my answer because I do not know the context in which the OP explains the reason.

They have the same exact goal that they are offering to potential funders: protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

1. First, they care about the result. Not the philosophy.
2. Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that it is surprisingly difficult for them to do so. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with expertise on those practical details. So being favoured approach would mean extra funding and not favoured would mean reduced funding. Making a yes or no policy decision should be avoided.
3. Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.
4. Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.

And lastly ...  from the long discussion in the comments because I probably should have mentioned this...

The thing is which of the reasons is most important depends on the person. It depends on which way you are looking at it at the moment. The others are then complementary to that. Different people in the same government will see it differently. Different people evaluating the same decision will see it differently. Same person looking at it in different context will see it differently. I specifically do not want to make this decision in my answer because I do not know the context in which the OP explains the reason.

They have the same exact goal they are offering to potential funders, protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

First, they care about the result. Not the philosophy.

Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that it is surprisingly difficult for them to do so. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with expertise on those practical details. So being favoured approach would mean extra funding and not favoured would mean reduced funding. Making a yes or no policy decision should be avoided.

Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.

Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.

They have the same exact goal they are offering to potential funders, protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

First, they care about the result. Not the philosophy.

Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that it is surprisingly difficult for them to do so. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with expertise on those practical details. So being favoured approach would mean extra funding and not favoured would mean reduced funding. Making a yes or no policy decision should be avoided.

Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.

Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.

EDIT:

From the long discussion in the comments because I probably should have mentioned this...

The thing is which of the reasons is most important depends on the person. It depends on which way you are looking at it at the moment. The others are then complementary to that. Different people in the same government will see it differently. Different people evaluating the same decision will see it differently. Same person looking at it in different context will see it differently. I specifically do not want to make this decision in my answer because I do not know the context in which the OP explains the reason.

They have the same exact goal they are offering to potential funders, protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

First, they care about the result. Not the philosophy.

Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that they are utter garbage at doing so and this has been demonstrated repeatedly in the past. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with actual competence. So being favoured approach would mean extra funding and not favoured would mean reduced funding, it is usually not a yes or no question.

Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.

Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.

They have the same exact goal they are offering to potential funders, protection of humanity from supernatural entities.

While their approach to achieving this and the philosophical outlook behind their decisions are entirely different this is not particularly important to the governments.

First, they care about the result. Not the philosophy.

Second, as a general rule politicians should avoid dictating or choosing the practical approach chosen for the simple reason that it is surprisingly difficult for them to do so. It is much better to fund based on the goals and the estimated odds of success and leave the details to people with expertise on those practical details. So being favoured approach would mean extra funding and not favoured would mean reduced funding. Making a yes or no policy decision should be avoided.

Third, they have no idea which approach is better and the only practical way to find out is to try both with reasonable funding. If they knew one approach to work better they wouldn't fund the other but they do not so they do.

Fourth, they do not know whether one or both of these projects will fail spectacularly. Both approaches taken have significant unavoidable political risks attached. Politicians do not want to be responsible if those risks actualize. If they committed to single approach, they would be responsible for that decision and thus politically responsible for issues with the chosen approach. As long as they fund both, they are simply experimenting and not committed to and responsible for either.