It scans your face in a public place in order to do facial recognition. What happens if I want to go to a public place WITHOUT having my face scanned for facial recognition and inclusion in some startup's dataset? Do I not get a say? Is that not my right? Where do we draw the line?

I don't know, by the same logic you could say you have a right to not let other people look at you in public (you don't). I understand the desire for a right to privacy (despite no such explicit right being anywhere in the constitution), but when you are in public, you be definition give up some privacy.

The thing is, I think most people who object to this so much would probably never even visit those bars where people care what the "scene" is like anyway

This. I'm having serious difficulty imagining that anyone would object this much if the bar simply hired someone to sit in the corner, count the men and women, and post the numbers on a twitter feed.

Because it's a very short hop from what's described here to full-on tracking, and some marketing company knowing where you are, what you're doing and who you're with at all times.

It's a similar situation to Google's street view - sure, it's in theory in the public domain, but when you start aggregating this sort of thing and making it searchable, it's different.

a bar is not a public place, it's a private place that the public are invited into.

Aren't bars more formally referred to as "public houses"?

sure, but public in "public house" (or just "pub") means open to the public, it doesn't mean that the public have some sort of right to access, whereas a public street means it's accessible by everyone.

Relating to the usage of the word public, humorously in England we have "public school" which is the American "private school", in America if you go to public school you're considered normal and in England if you go to public school you're considered rich.

If there were some way to assure people it only did what they say it does, and couldn't be modified in the future, I wouldn't really have a problem with it (bars are public places; at the very least, getting person-counts would be good).

Maybe they could skip the gender and individual profiling and do low-resolution IR, which would be a pretty decent way to identify human-shaped blobs. If you monitor entrances, you could assume no one dematerializes inside, so starting from zero, just count people who enter and leave to get a count.