Without question for me, cis-women have been the easiest to gain acceptance from. Followed by cis-men and lesbian women. Ironically though, a cis woman lesbian has been my partner for five years now.
For some reason, I think cis women have less to lose knowing a transgender woman, unless one of us used to be her boy friend or spouse. At that point we are playing in their sandbox and open to their life's lessons. We can exchange makeup and fashion tips quite easily. Having been down the same path and I think many cis-women are pleasantly surprised. Plus, it has always been great fun for me!
Men on the other hand are so sexually insecure, it is difficult to find one or any who will truly accept a trans woman. Although I know it happens because as a group transgender women provide an unique, even exotic look into sexuality for some cis-men. Those are the "admirers" who wouldn't want to bring you home for Thanksgiving dinner.
I my past, I have been alternately blistered or more often ignored by cis women lesbians. One of my worst gender slurs ever came at the hands of a butch lesbian at a big party. It was one of the few times I have let anyone get to me.
So, there you go. My personal look at public acceptance of transgender women. Especially important these days as we try to separate ourselves from the LGBT umbrella, be public and tell our story.