I don't really understand what the BoS achieve in terms of their hatred for synths in their ending. Sure they destroy the Institute and kill synths up to that point, but think about it. With the Institute destroyed is there really a way to identify who is a synth? The BoS didn't even know Danse was a a synth until they read the Institute's terminals with the holotape the SS gives them. Unless they make all of the Commonwealth line up for metal detectors there is no way to identify, right?

So, really are there any consequences for Gen 3 synths in the BoS ending? I'm not ranting about how the Brotherhood are terrible or whatever, just something I never really understood.

Really I have to agree with you on this. By destroying the Institute they make their goal of destroying the synths much more harder. But I guess their priority was to destroy the source of the synths at all costs. A possibility would be that the file you download would have a list of the synths? Though even if it did I doubt it would have them all. I guess anyone they suspect of being a synth would either be killed or have a X-Ray performed on their head as you see a ship in their brains (It think its their brain). or do as you said used a metal detector on suspected synths. Though maybe they will use the Railroads data to help track synths. This seems like a possibility but who knows maybe they planned on letting the synths die off.

Anyways there are a number of consequences for the Gen 3's:
1. They are either killed off or forced out by the BOS or the Commonwealths Inhabitants.
2. Integrate into the population and try to hide much like the Enclave remnants of FNV.
3. Fight back? Though this is very unlikely.
4. Maybe word will spread and the synths will head to Acadia (If it is still active).

Really anything can happen and in the next fallout game we will probably only at most hear little glimpses of it like for example "Crazy fight in a place called Boston" or something of that nature. So really we may never know what actually happened.

I guess its just a bad writing with plot holes up frontline, no offense to the lead writer Emil Pagliarulo, if only Emil Pagliarulo can understand what make Fallout is Fallout, try to immerse himself into the story he want to tell about, I am sure Fallout 4 could be the best action shooter storytelling open world looting ever made despite a great flaws; voice protagonist and the lack of role-playing mechanic.
to me, Fallout 4 ending is totally rip off from their previous Fallout 3 coolest moments when you choose to blow up the nuke in Megaton? seriously Emil Pagliarulo?!