I don't, but that's solely because we don't have gender neutral pronouns in french. But, writing in english, I use "they" as a gender neutral pronoun.
And oops, I just realized this is for non-trans people. Well, I'm trans, but I still answer.

I know maybe 7 or 8 trans women, but no trans men or intersex people to my knowledge. At any rate, no one has ever asked me to address them by alternative pronouns.

I don't like using them because I am not comfortable with their usage as well as I don't like the way they sound. Some people find it offensive that I don't use them, but its not something I feel comfortable with. I will switch pronouns back and forth between male and female with some of my friends.