Emulator

AF makes it look weird, but it's just doing what it's supposed to. If you play any 2D sprite-based fighter and turn on AF, the effects are very noticeable - the fighters tend to have horizontal and vertical lines running through them, like the Nintendo copyright here.

AF shouldn't be doing that. It's my understanding that AF should be filtering textures that are at an angle from the camera, usually textures down the road from the player, for example. I just tested with Four Swords Adventures to see if AF had any effect and it doesn't. So it seems to be working properly in some cases (I'd venture to say 'most cases') but in others cases it's filtering textures it's not supposed to be filtering.

The problem may be that the textures are stored by the game as separate pieces, which it throws together to get the full picture, especially for large textures. Here's a good example:

AFx1 - http://i.imgur.com/cgh5ukX.jpg
AFx16 - http://i.imgur.com/i2xBmwY.jpg

With AFx16, you'll be able to notice how the background is stored as 4 "quarters", but has the side-effect of making the text's shadows thicker. The pants at the top right is just the developer being super lazy.

My problem with this is, why is AF affecting these at all? They are not textures that need to be filtered by AF.

Sorry I totally forgot to reply to this. It only happens on the D3D backend, not on the OGL one.

There must be a way around this. PCSX2 seems to be accomplishing it just fine. Here I have screenshots of AF and forced texture filtering working separately in the D3D11 renderer:
http://imgur.com/a/Dq1D1