I believe trans women are "real women" in just about every way that matters. I only make an exception when I absolutely have to. For example, in sports, or in a medical context.
It might help to remember the word "women" is just a label we assign to people who share a certain common set of social and biological traits. And the majority of these traits trans women share, however in the case of trans women there are some exceptions. But it's not just trans people who don't fit cleanly into these groups, there are similar difficulties to be had with intersex people for example.
There are no easy answers here. Life isn't black and white. It's silly to think we can cleanly divide the whole of society into to clear categories.