I have heard of some peoples computers hanging when they boot and bringing them to an empty desktop or something similar, however there really shouldn't be any compatibility issues.
If any thing does conflict, it is most likely because both programs are running the same parts at the same time, such as real time shields for example.
If any parts do conflict, you just need to disable one of them. You can disable them like this:
Run Spybot S&D/ switch to the "Advanced mode" via the menu bar item "Mode"/ hit "YES"/ select "Tools" in the navigation bar on the left / hit "Resident" and there you can uncheck the checkboxes in front of the two tools.
Let me know if this helps. I have not used Avast for a while now as I have been using Linux lately.