No, you are not considered a bigot for this by anybody who is worth listening to. There are probably a few extremists for whom this is the case – like any extremist, their views are best disregarded.

But that's part of the problem here, and why this is a damaging article. It uses this view from a handful of extremists – "you are a bigot unless you date women with penises" – a view that almost nobody sensible would reasonably agree with, and then holds it up as an example of why another, unrelated set of things need to be fought against. This is a pretty common approach for people to use when trying to discredit or attack something they dislike.

I will add that Magadalen Berns, for what it's worth, was an explicit, out-and-out anti-trans activist. To quote her directly writing to a trans woman:

"You are fucking blackface actors. You aren't women. You're men who get sexual kicks from being treated like women. fuck you and your dirty perversions. our oppression isn't a fetish you pathetic, sick, fuck"

It is dishonest of Rowling to phrase this interaction in a way that doesn't at least acknowledge why her actions would be controversial under the circumstances. And this is a pattern that's repeated throughout the article. Let's call it an "appeal to reasonableness" – what seems like a reasonable and constructive argument on the surface only appears so because a lot of the context has been ignored or misrepresented.