I suggest Imaginary Evidence Fallacy.

I would call it motivated scrutinity.

In policing, illegal search often finds something. A way to harass groups you don't like is to expose them to searches with less basis. Searching a lot means you find a lot of stuff, even if it is cost ineffective or you had no reason to expect to find anything. The injustice a citizen faces when under this weapon is attention when its unwarranted.

I see the core of the algortih of the bias as: Do I like A? If yes, accept with suspension of  curiousity. If no, inquire about things connected to A. This has a high chance of stopping at a desirable state without needing to fabricate a single fact.

The way to resist falling into this is that if you are doing a detailed analysis, you should be even handed to be intereested in everything relevant to that depth. Be curious about the no and the yes.

If they had bothered to find something to support their preferred conclusion, we could call it confirmation bias.

Lazy confirmation bias?

Making excuses?

I notice that in notation form it’s just an extra ergo in the ordinary (p→q, p, ∴q) argument to yield (p→q, ∴p, ∴q). So maybe “ergotism” or “alter-ergo” for the name of the fallacy?

Rationalization