I have FF24 and real-time scanning on all the time and no problem downloading, which is what you should experience.
It could be that the source of your downloads isn't reliable and on some banned list somewhere or maybe you haven't got the normal Firewall settings for Firefox.
Open McAfee SecurityCenter and click Web and Email Settings > Firewall > Internet Connections for Programs
Click the word Program to arrange them alphabetically
Locate Firefox (they take a while to load) and make sure it has Full permission, using the Edit button if necessary.
If that doesn't help I would consult with Technical Support direclty. It's free by phone or online chat and linked under Useful Links at the top of this page.
You should never have to turn off any part of your protection to expedite any download. The only exception we advise is when installing Windows Service Packs.