By the 23rd century words such as 'gay' or 'straight' would be obsolete. People would just be people with lovers/partners/mates/spouses, regardless of sex or orientation.
No, there will always be words to differentiate between people. Words to differentiate between people of different colour, gender, sexual preference and so forth.
Differentiation in itself is no bad thing, I see no more problem with referring to a homosexual person as "homosexual" than I do with referring to a heterosexual person as "heterosexual".
Words used to describe the differences between people are not inherently bad and something should be done away with, differences are things to be proud of and celebrated - TREATING people differently due to those differences is where the problem lies.
Thing is, by the time of Star Trek, there will also be the interspecies aspect to relationships as well, not just gender, race or sexual preference.
There could be all new definitions if terms like "gay" and "straight" did indeed become obsolete.