In most cases, yes, we try to design electronic circuits in the sets we offer to ensure their maximum compatibility with the most popular models from other manufacturers. However, remember that the only way to guarantee full compatibility is to use exactly the same type of headsets. Different models of headphones (if they are compatible with the proper specification of the communication system) can work together, but it depends equally on the headphones themselves as on the type of on-board installation and how it was made. Different headsets can work well in one plane, but not in another.
The main source of incompatibility a headphones from different manufacturers is their is a different power demand of their microphone modules (microphone + preamplifier) and their impedances. Microphone modules need external power to work properly. This power is supplied from the intercom and if the circuits have different current requirements (which usually results from the impedance of the microphone used), one of them receives all power and the other gets nothing, so it does not work. Of course, in a huge simplification.