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.