Women are socialized into the feminine gender role from birth and thus have different experiences to those born male. “woman” is not a coat you can put on. A woman is an adult human female.
Transsexual and transgender people experience forms of discrimination and they are caused by the misogynistic, gendered society we live in; since gender is an artificial construct designed to keep women-as-a-class subordinate, any form of gender nonconformity is seen as a threat to patriarchal masculinity and therefore condemned- this includes being gay or bi, or not conforming to the gender role assigned to you according to your biological sex.
There is nothing wrong with gender nonconformity- I, and most other radical feminists, encourage people to do whatever they want regardless of the gender assigned to that behaviour (eg. wearing certain clothes, having certain interests) because we recognize that there is no reason other than socialization for males and females to behave differently and like different things. However, if a male subscribes to the ‘feminine’ gender role and claims that makes him a woman, that’s just reinforcing the idea that [x behaviour]=woman. This is problematic for women because we are trying to abolish this construct of gender, as it is the sole cause of the centuries of patriarchal tyrrany we have been subjected to. As an oppressed class we have a right to own the identity that has been forced upon us, and no one else has the right to appropriate that identity or the associated struggle.
So in answer to your question, no, trans”women” are not women. They are men who don’t feel comfortable adhering to the ‘masculine’ gender role. And that’s a-ok. In fact, it’s awesome to not conform to gender. However, appropriating the identity of an oppressed group of people with whom you don’t share the same experiences, that is offensive.