Very unlikely in my opinion. They are installed in separate locations and share no files.

Without knowing anything pertinent about your crashing problem, the first and easiest thing to try is to disable Thunderbird's Hardware Acceleration feature. It can be found at <Settings | General>, scroll all the way to the bottom, uncheck the "Use hardware acceleration when available" box. The option is designed to improve performance but, in my experience, doesn't make much difference and can clash with some display drivers.