Literally have no idea why anyone is sympathetic to synths.
Try doing their missions.
I didn't even realize that was an option without siding with them immediately. Like, BoS guy got mad at me for failing to secure their trust in order to blahblahblah, and I didn't know what happened, because I just said F U when I went in following the teleport and decided I couldn't stand cooperating with them.
But I loaded that save and went back and found that they actually have a storyline that presents them as justifiable, at least from the way they perceive things. They give absolutely no credence to the people who live on the surface, but that's also because they think life on the surface isn't all that sustainable and that furthering mankind is never going to take place in the wastes.
I mean, they are sending synths with "By order of the institute you must all be destroyed".
I saved the girl at covenant (didnt kill the dr as she never went hostile). But, I hear she actually was a synth and seeing how synths infiltrate settlements and murder settlers, I can't see how people justify Synths sympathetically at all. ---