I'm both fearing and hoping this is something driver related, we've had a number of people with AMD carts report similar things lately...
Things that might help you: the -no_vsync flag seems like it has sometimes had an impact. If it doesn't, you may also need the -no_fps_capping flag. Thinking about things that have changed relatively recently in the engine, it might be productive to try -noenv and -no_deferred as well. Either of those last two would have big visual impact when removed and it's definitely bad if they're the issue, but if either fixes it entirely it'll be suggestive about problem areas.
Things that might help us hunt this down: Definitely let us know if any or none of those flags helped, naturally.
If you have patience for more troubleshooting, debug logs would be very useful. You generate these by playing in fastdebug, which you can use via the dropdown menu button in the bottom right of mod cards. Then in the same interface there'll be an upload debug log button that'll give you a link you can post here. Simply starting the game, loading a typical mission and exiting the game immediately after should generate plenty of info. The following debug logs would be ideal...
A well-preforming mod (fsport)
A poor-preforming mod (b5?)
Check a mod that hasn't updated much recently such as DE, run it(in fastdebug) as you normally would, then again after having used modsettings to pick an older version of FS2. If an older version runs significantly better, having both debug logs would be useful.
If going back to old engine versions doesn't work, you could also try rolling back to older GPU drivers.
If you can't do all or any of that, I'd entirely understand. Unfortunately there doesn't seem to be many AMD cards among the devteam, so it's hard to get any of this kind of investigation done ourselves.