Well, I'm definitely sexist. And ageist, racist and prejudiced in all manner of ways, only some of which are known to me. I might wish I weren't and try to think cautiously to mitigate it, but I do acknowledge I am this way.
With respect to authors, I think I'm liable to make assumptions that I'll be less likely to enjoy the book if it's a female author. I don't enjoy 'girly' stuff very much and it impacts my enjoyment of the book. For example, The Hunger Games was an otherwise strong trilogy, but the love triangle stuff was unfailingly annoying. I've never had anything like that from a male author. I'm not sure how much of this would be explained by past experience and how much from prejudice.
With respect to identifying with characters, I do think I empathise more readily with male characters. I think this is because I have less patience for stereotypically female concerns and behaviour, like love interests, indecisiveness, weakness of will, etc. I most enjoy characters whom I perceive to be worth emulating, and often female characters come across as weak and I don't empathise with them very well. I want them to be stronger, cope better and stop fretting about inane things that I, as a reader, don't care about. But these can be criticisms of characters that can be potentially male or female; I'm not sure if a character's gender alone would affect my ability to empathise with them.