You can support the rights of trans people to live life free from violence and discrimination, to go about their everyday business without having to disclose or answer awkward questions about their gender for example, support the rights of all people to wear what they want, etc, without being contradictory to feminism. Indeed many radical feminists would agree that a person's gender is irrelevant to most parts of life and shouldn't be a problem.
The difficulty comes in the few areas where trans rights and women's rights are at odds. For example some transwomen believe that in order to be accepted as female they must have access to female only space. But most female only space is created for reasons of protection against male violence or specifically to discuss the lived experience of being female and growing up female, which transwomen don't have. Their lived experience is undoubtedly also difficult but it is different.
Another point where transgender rights and women's rights clash is women's recognition in sports. It's not fair that a trans woman, who has male biology is counted as female. It undermines the reason for separating the sexes in sport.
Lastly it's a problem for women's rights when transgender people commit crimes and are recorded as their transitioned gender in statistics rather than their natal sex, because this causes problems in recording and assessing patterns and trends of male violence against women.
Sorry my phone keeps separating the words trans woman, not me.
In short the problem is not transgender people in general, the problem is that sometimes transgender rights and women's rights are fighting for different things. I do support trans people but where there's a clash I will come down on the side of women's rights because I think this is still important and necessary.