Yet at the same time, they have absolutely no problems approaching Nick Valentine who makes no effort in disguising his synth identity and getting him to solve their problems.
Huh? Double Standards much?
I'm pretty sure that's exactly the point.
Nick makes no effort to hide who he is, and doesn't try to 'pull the wool' over the eyes of the people of Diamond City. He's a synth, and he owns up to it.
What people are really afraid of, are the synths that take the places of people they know/love. The infiltrators who look just like humans.
Its the same reason that there's a altmer selling wares in the market square of Windhelm. People are able to get through the prejudice and earn peoples trust because they have something useful to the community. It also helps that Nick is full on terminator looking, and not human-like. All of the institute synths with the terminator look ive encountered so far just open fire on anyone that comes near, and when they see both a synth with a individual personality that's not firing those strange energy weapons then im sure it naturally got people curious.
Its also compounded by the fact that for a city so afraid of synths, Nick is the closest they've got to a man on the inside. He may not know much, but even with the little bit ive been through the main story its been setting him up as a major ally of anyone who would oppose the Institute. If there's a problem with a synth inside their ranks, old Nick will be the most qualified to figure out who it is.
If you keep him as a companion and do things he likes, eventually you'll open up a dialogue between you and him where he explains his past and talks briefly about why the people of diamond city accept him.
Yes I must admit, first I thought Nick originally DID look completely human, but his hand and face and possibly other parts were damaged by the girlfriend of the 'gangster' with that baseball bat. I managed to convince her to leave and then left myself, but i just assumed that he was going to get all that repaired before he got back to town. Hes now following me around still looking more robot that Human and it did get me wondering why people were not treating him poorly. I even took him to Concord.
This.
Also, he arrived at Diamond City quite a long time ago and was already largely accepted by most of the populace before everyone got terrified about synths replacing real people.
Nick tells his story why when you get to know him
As someone said he doesn't hide the fact he is a synth and people fear is getting replaced by a synth(or someone they love being replaced by one)