Just found them and the leader is asking me if my character would save a Synth at the risk of her own life. She wouldn't accept a 'It depends' response (which I thought was the appropriate response to this question), saying that it's either 'yes' or 'no'.

Really? I think it actually DOES depend on the circumstances. If a Synth were trying to kill my character, no, she wouldn't try to save it. If, however, a Synth like Nick Valentine were in danger, sure, I could see her trying to save him. It all depends on the circumstances, chiefly among them: "Is this Synth my enemy presently?"

So now I'm wondering how I should respond to this question, and also, is the Railroad seriously this black and white about the issue? I'll just join the Minuteman or the BoS instead if that's the case.

The Railroad is a bunch of fanatics.

But if you frame it as.

"Would you risk your life for a slave"

Then you understand their perspective. They have the view of Synths as human beings under a horrific tyranny, they need to know if you're all in.

Of course, that doesn't prevent Synth soldiers of the Institute from killing you.

They do want to know your stance, though.