Accusations of hypocrisy is only an ad-hominem argument; i.e. a fallacy.

Lol, no. Hypocrisy is a type of lying. You say you care about something for a reason, but actually only care about it for another often less persuasive reason.

You see it all the time in politics where people are outraged at X when the other party does it, but can't be assed to care when X is done by their own party. They're lying that they care about X. The truth is they're using it as a lie for political power.

I don't agree, but even if you were right, how is an accusation of lying still not an ad-hominem argument?

- "I think that this other person did a bad thing X."

- "You're lying, your other actions show that you don't really think X is a bad thing."

How is that an argument? The issue was originally that some other person did a bad thing X, but the second person above changed it to attack the first person making the argument, and accused the first person about lying about what they really think. Is this not an ad-hominem?