I don't believe in the concept of gender outside of a social construct used to oppress the sexes. I am a woman as in adult human female and my behaviours and personality have no bearing on that.
Transpeople believe gender is innate and they are a woman if they say they are. I'm willing to agree that the concept of a woman as a social construct does exist, but my thoughts would be that we should destroy these gender roles rather than reinforce them through the whole 'trans' concept. Because it's sexist and harmful and limiting.
So I don't agree with their philosophy but I can't say that what they are experiencing is not real or whatever because, well, it's real to them.
So much like any other belief I don't share, I can respect them whilst also asserting my belief and speaking up when I think they're beliefs are infringing on the rights of others. They can be a 'woman' in terms of a nebulous set of stereotypes that I actually find offensive, but they aren't female, and being female ought to be a protected characteristic for a multitude of reasons.
Some transwomen are saying they are female and need to be treated as such in every way in society which is simply ridiculous. Transwomen and females might both be women but they are completely different groups that have different issues, needs and vulnerabilities that mean being male or female matters and is not an identity.