That thing I said, "There's nothing about being trans that makes demands on other people's orientation." I'm not changing my argument, but I can see how people may see trans as a threat to their orientation. Or gender for that matter! (I suppose this can be called a form of cultural or personal insecurity.) So I'm going to try to be gracious and stretch that out and play with it a little. Though... Point remains, that this is not a good defense for the owner.
I've only seen a couple articles and I don't know what 'flavor' of trans these gals are, that is assuming they each have relatively consistent styles from day to day or for when they go out to places like this bar, whatever it is like there. For all I know, one of them might look like a geeky tomboy and another might look like a classic blonde Barbie doll. Just as likely, if not more, they're a lot more "average" than that in many ways -- at least if people outside their circle are actually looking for anything "normal" when they scrutinize, I mean after they have done the common double take and picked up "oh, hmm, trans."
The thing is, whether it's because they are scrutinized and talked about by others or because they talk about gender and maybe pick at it among themselves or with others.... Trans often end up showing other people things about gender they aren't comfortable with. Sometimes these are sexual details of many kinds, and sometimes they could logically be about where so many different gender options lie and how they work. But many people have been trained to file much of gender questions under "sexuality" also... And you know how "well, okay, that's potentially also involving some sexual choices" can often become "oh, c'mon it's always about sex" for anyone else you meet when they aren't completely on the same page. And this brings us to situations like the owner saying "not a gay bar" etc.
Getting to the point, I wonder if the trans girls bothered someone merely by speaking about being trans or about topics like how cis or straight people think, or perhaps even "how I used to think about sex/girls before I became out as trans" etc. etc. I mean, these are things that can make cis and very heteronormative people uncomfortable, because they sometimes really expose or make fun of how the traditions of "straight" are often put together. And then you have some girls -- in a group, now! -- who may or may not pass in so many ways, sometimes being checked even more closely than other women.
So I'm not denying that some people may get uncomfortable around trans. But so what... I get uncomfortable myself around some Black people, but I don't think that means the owners should chase them all away simply because I am bombarded with stereotypes in the media, and I don't know heads or tails about where they came from or what their way of speaking means.
As to ideology, being trans and sitting in a bar is not an active billboard waving protest any more than being vegan, or being Black, or wearing Nikes, or that cis guy talking about his girlfriend(s), or whoever talking about Edward Snowden with any given person in the bar. If you make living or speaking about trans out to be ideology, then the only question is, "Well, where does freedom of speech end for everyone at some point that others can't stand it or will blow up and wreck the place? Does every group have to declare its own private, exclusive venue and fund it in order to go out, so there will be no publicly open areas, until they break down to the smallest possible units and damn the economics of scale or any notions of a public commons?"
As far as sexuality... The trans being there, whether with many gender curiosities or few visible or audible, are not "imposing" an orientation on anyone any more than the state allowing same-sex marriage is forcing anyone to have a same-sex partner (let alone to marry one)... But oh, some are apparently so upset that they can't control themselves around trans?? What! Well, this is nothing new I suppose. A good few men apparently think women in general are responsible for most of their rapes, too...
Finally, what an impossible thing to police anyway -- gender! Some women have big arm and chin bones or small or no breasts -- who knows at a glance, if they are trans or not? Should they all be thrown out so that the owners can show they have done their best to eject everyone who might be trans? (Or were they going to require a show of birth certificates at the door to confirm original, relative penis length?) I don't think so.
........... I just think these are all inappropriate things to be targeting people over in an open to the public establishment.
Maybe there is another category for membership only establishments that have limited access based on demographics somehow, I'm not sure. If they are legal, then I think even those would have to establish their rules openly and periodically through some formal process --- not a targeted, private phone message to previously accepted customers.