I don't see a problem with the situation you present, I think you just need to make a couple tweaks to how you interpret what's going on.
Every god has different representations and images around the world, but this is unknown to the majority of the population
So far you haven't actually mentioned that the god's real shape actually changes. Then perhaps it doesn't. What I mean is, what changes is only the image of the god that the mortals have. The true form of the god is something more general and abstract, a concept, a mind. They still have their intents and personalities but aren't really tied or changed by the way the mortals portray them, and may have their own true or favored forms.
Gods can be worshipped in different forms because they all ring true to the god's core ideal. The bull and the female strategist you gave as examples can both represent the God of War, as they both carry the idea that "You and I have a disagreement and we are solving it in the field of battle". That is how that God thinks things should be settled, and as long as those forms ring true to this, they will hold some power.
So, why is it relevant how the mortals portray the gods?
Well, the gods are real in your world, so I assume they have some effect in the world. The blood sacrifices the Bull War God receive will confer the warriors some boon in battle. In turn, the generals being inspired to find better solutions and strategies will have to attain to that manifestation of god's honor code. No backstabbing, no backing down from someone who affronts your honor, or you lose your god's favor. There is a cost and there is a reward. Different forms will have different rules for this, that all fall in line to how they are represented.
They all work cause they are all true facets of that particular god, the god doesn't care which one is being worshipped and believed in at the time. Why not worship all at the same time then? Well, perhaps some mortals could hold and accept all those ideals in mind, but most would not hold on to and believe each facet as strongly. The same way they couldn't comprehend the true form of the god. That's why simpler, defined manifestations that take on ordinary, worldly things are generally more effective.
With this knowledge, priests (at the orders of a ruler for instance) could sway the impressions of the worshipers to get the aspect of the god that better suits the kingdom's needs. Do you want to subjugate neighboring tribes? Make the Bull form of the War god gain believers. As you consolidate your power and control more land and face stronger adversaries where brute force doesn't cut it, transition to the General aspect. This works more smoothly if it is planned beforehand.