When is a “what if” a fallacy?

I hate claims that are presented to be objective but then is based on speculative “what if’s”or highly unlikely but possible, it seems like wishful thinking or usually being contrarian for the sake of it. Conspiracy theories of course are the extreme form of this. “This happened but what if the government covered it up”. Where is the line drawn ? 

This would be in the class of "fallacy" that is more of a manipulation or rhetorical technique. When hypothetical is presented, it should be given consideration in proportion with its probability. For example, if I said in response to a claim that vaccines were effective, "what if you're one of the ones who experience bad side effects?" Then based on that possibility, we can explore that possibility for a moment or two without being unreasonable. However, if I were to ask, "what if you drop dead right after getting your shot?" Then the question is less reasonable to consider at which point it becomes more of a tool of manipulation to instill fear than to pose a sincere hypothetical that is worthy of due consideration. Intent has a lot to do with the fallaciousness. In this example, someone could be misinformed or extremely paranoid rather than deceptive.

Alex answering Alex… lol. Anyway, possibilities are infinite. One could make up any  ad hoc explanation of anything. It’s important to remember that just because something is hypothetically or even epistemologically possible doesn’t mean that it’s true. It’s possible that the universe was born on the last Thursday. It’s possible that the simulation hypothesis is true and that aliens are laughing at us minions now. It’s possible that Jesus magically ascended to heaven without the Jews seeing him (perhaps by making himself invisible to them but not to the disciples). It’s also possible that the government is covering up everything. So what? In determining what’s most likely to be true, it’s better to evaluate the probability of something, not the possibility. That the government is making things up is possible, but if the data we have strongly suggests that they’re saying the truth, then we may safely dismiss the possibility of it being fake based on rational grounds.

I hope this helped.

The other answers are good.

If you're looking for a specific fallacy name, then this is the appeal to possibility when argued in the form:

X is possible.

Therefore, X is true.

or

X is possible.

Therefore, X is probably true.

It could also be hypothesis contrary to fact, when argued in the form:

If X did/did not happen, then Y would/would not have happened (based only on speculation).