Nope. That's just not true. Remove Curse can be cast by any old drunk who can cast Remove Curse. Any Cleric, of any god - including other goblins, with Goblin religions. Any Paladin - including evil and scary ones. Any Wizard or Warlock who knows it - so not every arguably religious people.
Further, it doesn't require any conversion. A Goblin who hates you before you cast Remove Curse on him may well still hate you. He just won't hate you because of a magical curse, but because you, he, or both are jerks. There's no baptism or oils on forehead. There's no accepting Lathander (or whoever) as your Lord and Saviour. There's just a Wizard or whoever going ZAP with their one-action casting time, which could be done from surprise or whatever, and BAM, curse gone, but that's all that's gone.
If Remove Curse could only be cast by Good or Lawful Clerics, or something, you'd have a point. If it required some sort of elaborate ceremony or agreement from the target, you'd have a point. But that's not the case. This is a spell that, sure, could be cast by some conversion-minded would-be missionary-priest, but could equally be cast by a drunk Wizard down a dark alley. Hell, you could put it in direct opposition to "missonary" stuff by having the main people casting it be other Goblins, keen to free their fellows. And those Goblins don't have to be nice guys, signed up for friendliness and hand-holding, either.