Which mods disable achievements?

[wrillexx]

Hi, im new to mods in Isaac and ive heard that not all mods disable achievements. Is this true? and how do you see if a mod disables them? i want to keep unlocking stuff but would also like to play with some mods to make things more interesting.

[The Renderer]

You can use any mods after defeating Mom at least once.

You get an icon with a crossed out trophy on the left when you cannot unlock stuff (and achievements).

[Nazemec]

Rephrasing the answer to fit the title:
All of them before the first Mom kill on that save.
None of them after that kill.

[HeraldOfOpera]

Further stuff people haven't noted: certain mods may end up accidentally disabling certain achievements for reasons that are only obvious once you've looked at the code. For instance, the "Always Void" mod disables Mega Satan unlocks as collateral damage from overriding the normal ending to that fight.