Those three sound completely different to me, as far as how I’ve been pronouncing them goes. “Their” doesn’t have the extra lagging e sound (as in the e in err) in “there” where I curl my tongue upward at the end. “They’re” preserves the ey sound in “they”, just concatenated with an r as in err sound.

When I say, “They’re there,” people can make out what I’m saying, though as more people seem to tell me that these are just homophones, maybe they’ve just been relying on context.

Don’t phuck with my head, I’m two drunk!