That's likely a result of some process running in normal mode startup that is not running in safemode.
You'll probably need to perform some
Diagnostic Startup steps to chase down the offending product, but....
If it was me I would start with Avast. Remove it completely from the machine by first using the programs and features applet in the control panel and follow that up with the vendor specific
Link Removed reboot the machine even if not asked and see if the browsers start behaving better.
Regards
Randy
EDIT: And yes you can have multiple browsers on your machine (I have five), and no, I have never experienced any cross browser conflicts as I frequently have two or more running at any given time...