I will put it as plainly as I can.
First Agnitum Outpost Firewall Pro has never had an adverse effect on avast on my system and that is going back from version 3.0 through 7.5.
Second Outpost will detect Avast if you have it installed and ask for confirmation that you have it installed. When you acknowledge that it will offer to run in Compatibility mode, disabling the Web Control and Anti-Spyware (as avast has both covered) and to avoid conflict. Why otherwise would Outpost suggest it.
So that is why you should install avast 'first' followed by Outpost firewall pro 7.5. I would go a step further and suggest that you do a Custom Install (may be called expert install or words like that), Outpost will still detect avast, but you have greater control of what gets installed (not just disabled) so you should uncheck the Web Control and Anti-Spyware modules so they aren't installed.
Outpost during the installation would have you exclude the Outpost program folder, cheat and say you have as I don't feel it necessary to do this. I do make one exclusion in avast, File System Shield, Expert Settings, Exclusions and that is for C:\Program Files\Agnitum\Outpost Firewall Pro\wl_hook.dll and nothing else. I have had no problems in the past 7+ years like this