When I park my bike in 1st gear and try to move it later with the clutch in it rolls very heavy.
My clutch fluid is pretty dirty but my water level stays the same and the clutch works perfectly fine when the engine is running.

Any ideas?
(I do wheelie often using the clutch but don't abuse it)

I never had any problems putting the bike into neutral.

Sounds like I should pop the clutch cover to check these things. Does that require a new gasket or just the liquid type?

If you are careful you shouldn't need to buy a new one.

I'd bleed the clutch master and slave before going into the clutch. Sounds like a change of mineral oil is required anyway.

Will do what Klincky says first

If you put the bike in first when cold with the engine off and try and push it it will be hard to turn. Mine has always been like that. Clutch is fine, working how it's supposed to. Just cold thick oil dragging on the plates.

Tbh I wouldn't bother trying to fix a fault that might be not be there. Unless you need to shove the bike to work in gear for some reason.