I carry approx. 30 different term thermostats from all of the various brands. I have the close one or one pretty close to it most of the time. As long as the temp is the same or very close (within 10 degrees), I will use it. Never had any problems. Same with the timers. As long as specs close, they will work fine. Take the Amana thermostat, for example. It is the one with the brown and orange wires. I use a GE 50x50 as a substitute for that one all of the time and it saves the customer money. Never had a callback on that.
I have a Parts box and keep all of them in one box. When I work on these, I carry the entire box into the house. Makes it easier to match up thermostat if I have to use a substitute.