By the 5E Rules as Written, It Auto-succeeds
Remove Curse doesn't call for an Attack Roll nor a Saving Throw, so--per the PHB, it auto-hits and is automatically effective.
D&D 5E encourages DMs to 'fill in the blanks' when they find it necessary. The PHB appears to assume you'd never want a beneficial spell to fail when cast on you...but if that's the case, a DM may freely invent rules for how that works.
It is neither unreasonable nor without precedent that you could resist a beneficial spell if you didn't want it. And this sort of thing has actually come up in my games. (Players were fighting against friendlies who had unknowingly become infected with lycanthropy and shifted while they were traveling together; the Cleric opted to just start spamming Remove Curse).
In that particular case, I ruled that the Cleric would have to make a Spell Touch Attack. Remove Curse has a range of Touch so, presumably, you have to touch your target in order to cast it. An unwilling target may not let you touch them voluntarily. This worked out well enough...it allowed the Cleric to still attempt to save the party's friends, without making it an instant once-per-round auto-success.
Since then, I looked back at the 3.5E rules and found this little nugget in the SRD for the Remove Curse Spell...
Saving Throw: Will negates (harmless)
This is the standard pattern for spells as written in 3.5E. Even beneficial spells had an option to resist them if you didn't want the spell. So if you need inspiration for how to handle this...looking back down towards 3.5E could provide some guidance beyond my own experience with it.