Both men are waiting to be tortured, probably to death. Gerbier makes a quick mental assessment of his fellow prisoner and decides to use him to help his escape, which might enable the other man's escape too. The other man seems to me to have an inkling of what's at stake and that's why he goes along with Gerbier. If one of them makes it alive this matters more than who it is and that it's Gerbier is fortuitous.
Movement ends, intent continues;
Intent ends, spirit continues

I took it simply as a warning, so that the other guy would also be ready to make a move, instead of just freezing there, surprised, not knowing what to do.
Never be complete.

It was only logical to let the other guy go first since he was going to be struggling with the guard. Since they were both going to run for it, there is no way to tell who is going to have the advantage, the first one out of the second. In this case, I thought too that perhaps he had calculated the first one out would create a diversion but he couldn't know that for sure. For example, what if the guards out front had not left their posts? (In fact, wouldn't that most likely be their orders; to not leave their posts?) In that case, they would be much more prepared to deal with the second person running out the front door, would they not?

Considering his apparent nervousness upon submitting under the razor after having noticed the pro-German message on the wall, Im pretty sure he had no idea what the barbers ideological affiliations were.
"facts are stupid things" - Ronald Reagan

You know there was another aspect to that escape. After knifing the guard (ooohhh!)and running like hell from the Gestapo he slipped into that barbershop where the barber warily eyed him as he came in. I don't know. Was Gerbier just lucky there? Or perhaps did he know that that place was "safe" especially near Gestapo headquarters?

I also had that impression. To me it appeared that Gerbier, the engineer, calculated the escape sequence and hence essentially threw the anonymous Rsistant under the bus to improve his own chances for escape. These were hard men in hard times, times that demanded morally questionable actions. That is underscored by the final scene.