Well I don't know any women in real life who think like this.
The fact that you don't know anyone who is considering changing their voting habit proves absolutely nothing. The fact that there are people on here who are considering it, however, shows that it is happening.
Let's correct a few things
You may, of course, give an alternative POV, but that is not the same as 'correcting' things 
It is not necessary to use a qualifier every time you mention a group of people, and unless there is an implication that the behaviour being described is universal there is no bias. Do you say 'flowers are growing in my garden', or do you point out that not every flower is there, but only some?
Some transwomen have said lesbians should be open to relationships with them.
Not all transwomen identify as lesbians (or are autogynephiles), so again, there is no need to qualify what I said - at no point did I imply that all transpeople were doing anything at all. The point, though, is that I wasn't talking about the ones who said that lesbians should be open to having sex with them, which you have shifted to. I was talking about the ones who insist that if a woman enjoys sex with women they should enjoy it with them, despite the fact that they have intact male bodies, and get very unpleasant when they are rejected. 'Suck my girl dick' sort of unpleasant. Not all transwomen do this, but how many have to do it before it is necessary to point out each time that they are a minority?
Some transwomen are involved in sport
And many are not. Is it really necessary to point that out? It is also true that not all transwomen cheat at sport - that goes without saying, too. The point is that those who do are at a huge advantage over women who have trained for years, and this sort of cheating can only be dealt with at a high level. When politicians refuse to recognise that a man saying he is a woman so that he can beat other women at swimming (or whatever) 'some' people find that unconscionable and feel reluctant to vote for them.
Some companies encourage people to declare their chosen pronoun, a bank has given employees the option of having their preferred pronoun on their badge.
More than one company has 'encouraged' people to declare pronouns. Are you really unaware of the trend in universities, local government and other 'captured' organisations? It is widespread in the public sector. Just because the Halifax Bank has made the tabloids doesn't make them the only ones to be doing this, whether on badges or in email.
A few people are getting all het up about it and posting negative and biased views about transwomen. The very nature of bias and discrimination is that you accuse a whole group of people of behaving in a certain way and don't recognise them as individuals.
Bias is shown when terms such as 'all het up' are used to minimise the feelings of those with whom the writer disagrees. That sort of bias is usually used by those who dislike women, as are many of the arguments of the 'allies', such as pretending that it is age that makes critics think as they do, without recognising that people think for themselves and come to their own conclusions by weighing up the arguments in their own way.
Language is important, which is why some people get annoyed when it is mangled - when 'mothers' become 'birth givers' and 'women' become 'people with vaginas' or 'people who menstruate'.
As M0nica says, there is an issue when 'some' (used here to mean a small proportion of the whole) are forcing their views onto 'most' (used here to mean the majority) people, so 'some' people will speak out about it.
