I agree with what Mary Morgan has said. It's bias that is taught within society that makes many women unaccepting. In the past two decades, I have seen a clear increase in the level of acceptance.
Children have no problem with crossdressing or crossdressers until someone, usually an adult, tells them that they should. I'm finding that fewer children now take notice of such bigotry, and fewer parents appear to be teaching it than even 5 years ago.
I would agree with the statements "Many women don't currently accept" and "A few women will never accept" but I don't believe that the word "majority" is correct even today, and as society is gradually becoming less bigoted against us, the proportion who don't accept is diminishing.
I know a few women who have no problem with men who are not their partner being crossdressers, but would have a problem if their partner was. The number so far is 2 in over a 50 women that I have asked this question of over the years.
As with the fear of rejection, ridicule, etc from going out in public or being out about crossdressing, I would have to say that "The majority of women will never accept" is a pessimistic perception in the mind of a crossdresser.