Your beliefs, Strongmummy, are frequently found among those who haven't investigated the issue or are working on out-of-date information. It used to be that transwomen were extremely dysphoric men who had all the surgeries and who were not sexually attracted to women. Things have changed a great deal. Today's TRAs call the old-fashioned transsexuals "truscum" and pride themselves on their ladysticks with which plenty hope to penetrate lesbians.
Most transwomen do not think they were "born in the wrong body" (which is, in itself, a nonsense), they aren't dysphoric, 80% of them have - and plan to keep - their male genitals and over 70% are sexually attracted to women.
Given these facts, is it unsurprising that women object to sharing showers etc with what many of us (including old-fashioned transsexuals) would describe as men in drag? To add to this it is well-known that some transwomen, generally late transitioning, do so to gratify sexual fetishes. If you don't believe me, I suggest you spend some time investigating the Reddit subgroup r/asktransgender where a search under terms such as "panties" or "tampon" will prove a real eye opener and all in the words of transwomen, not us mean feminists.
You might be better informed as to current issues if you Google "cotton ceiling", a nasty piece of rape culture wherein lesbians are shamed for not being prepared to have sex with males. Some transwomen who want sex with women are happy to define themselves as lesbian. Lesbians are not happy about this.
Women opposed to trans ideology don't want trans people to face discrimination in employment or housing. We do not, however, feel that women's interests should - as always - go to the bottom of the list, beneath males however they identify and women who claim to be men.
Plenty of posters on the Feminism boards started off with your opinions, Strongmummy. As the evidence piles up they change their mind. Currently trans activists are pushing for a misogynist and homophobic agenda.
Given that research demonstrates that transwomen commit sex and violent crime at the same rate as other men, and it's no wonder women are fighting against the intrusion by transwomen into spaces that are female only for reasons of our safety and dignity.
There is no evidence that transwomen are more likely to be attacked than women. They aren't. Transwomen who are sex workers have a very high chance of being attacked, but this is in comparison with men, rather than female sex workers who are also at high rate of attack.
Those who accuse women of transphobia also add to this a claim that no transwoman has ever committed sex or violent crimes against women and girls. This isn't true either. A transwoman is currently on trial for a particularly brutal murder as we speak.