As a GM, I use some revenants for my campaign. Those revenants all have class abilities and 2 are spell casters (an abjuration mage and alchemist artificer). The "problem" (it's not a problem, but an "and what if they do that?") is that they can use the Protection from Energy spell, so they can have fire resistance.

They have a Regeneration feature, with the following rules:

Regeneration. The revenant regains 10 hit points at the start of its turn. If the revenant takes fire or radiant damage, this trait doesn’t function at the start of the revenant’s next turn. The revenant’s body is destroyed only if it starts its turn with 0 hit points and doesn’t regenerate.

My question is: What happens if they gain fire resistance (or radiant resistance)?
Would they lose the weakness that prevents Regeneration from working when fire damage is dealt?

Nothing changes, except that the Revenant takes half damage from fire.

The Regeneration trait states:

If the revenant takes fire or radiant damage, this trait doesn't function at the start of the revenant's next turn.

Just because the revenant has fire resistance doesn't enable him to regenerate despite taking fire damage. It makes some sense to think that the Regeneration trait is vulnerable to fire and fire resistance would cancel that out, but that's not the case, since nothing in the rules says so.

The only case where fire resistance would allow the Regeneration trait to work as opposed to without resistance is when you take exactly 1 fire damage, and the resistance halves it to 0 - meaning you didn't take fire damage, and therefore nothing prevents the Regeneration.

By the rules, resistance doesn't matter

Revenant's regeneration is suppressed when it receives fire or radiant damage. Since the revenant still receives fire damage, the resistance doesn't protect it from losing its regeneration, except in the unlikely scenario where the revenant would take a single hit point of fire damage before the resistance was applied (in which case the revenant'd take no damage and therefore wouldn't lose their regeneration).

Being the GM of your game, it's up to you to figure out how you want these revenants to play out. As a general caution, many rules that applied to a monster may stop making sense after the monster is augmented with class abilities and other such new features. You've already changed the creature so I wouldn't worry about being careful to respect the original regeneration rules.

However, if you change the revenant so that it can gain fire resistance, and choose to rule that fire resistance also protects the revenant from losing its regeneration, you ought to give your players a fair idea about this and make sure they have the means to combat the revenant. They are near-indestructible without fire or radiant damage, and depending on the party's composition, the player characters might have inadequate means to fight if one of these is ruled out.

What happend if they gain fire resistance (or radiant resistance)?

They would take half damage from fire effects, but still affected by all additional consequences when they are included in a description of a fire spell or monster feature etc. That includes consequences based on any of their monster, race or class traits too as the target.

Do you think they loose their regeneration weakness (that don't work if fire damage were dealt)?

No. The fire (or radiant) damage keeps its type.

The only way to block the regeneration weakness would be to gain immunity to fire, in which case no fire damage would be taken, and the regeneration weakness effect could not be triggered.

However, it is quite a pragmatic thing for a revenant to use magical protection from fire if it is available. If they have resistance to fire, then either they take half damage from at least one attack per round or they regenerate on their turn. Enemies that know about a vulnerability will target it, so resistance to fire is likely to get a lot of use for a smart revenant character.