Doing something like that can effect play, yes.
If the PC who intends to play a lecherous dwarf or hopeless romantic of an elf finds out either of those races has some drastically different biological set-up from what's expected, then it can very well matter and effect play.
In general, I don't deviate much beyond what the creature most strongly resembles. PC races, therefore, won't be too much different from humans; minor deviations, possibly, such as reduced or increased birth rates, a higher propensity for twins, longer or shorter pregnancies, but nothing too big.
As such, I'd be disinclined to accept the idea of gnome hermaphrodites or any such thing with most non-monstrous humanoid races.
Things like thri-kreen or even merfolk or the like, though, and things change. But a generally human looking creature will have a generally human reproductive system in my games and in my general mindset; if told the hypothetical kuo-toa I wanted to play would spontaneously change gender under the right circumstances, I'd be fine with it. If I were told the same about an elf, I probably wouldn't want to play an elf and wouldn't want much to do with them in the game in general.
If I'm looking to play something really different from the norm, I'd play something really different from the norm. As it is, most PC races don't qualify for that for me, thus why things like that wouldn't really float my boat.