wait, are they red like that in game?

or are you circling something? I can't tell what you are if you are

edit: oh I see it, forget everything, Lange is smart

try mat_trilinear 1 (and reload the map / type retry after putting that in)

edit:
Doesn't look (at least on my computer) like mat_trilinear has any effect when mat_filtertextures is off. So you might be SOL if you like the blocky texture appearance, but if you're fine with them being more smooth/blurry you can use mat_filtertextures 1 with that and it'll work.

The effect you're seeing is the game progressively halving the texture resolution at distances where a single onscreen pixel would be the result of four or more texture pixels anyway, which is called mipmapping. Trilinear filtering means the game will interpolate between the two mipmap levels it's between instead of using only one at a time and switching at exact distances. It's called trilinear because it's interpolation on one more axis than bilinear filtering, which is the smooth interpolation between texture pixels that makes the difference between blurry looking textures and blocky looking ones (a difference that's easy to tell with FPS configs that use low res textures to begin with (actually just forcing a minimum level of texture halving aka mipmapping)).

Really there's no reason it can't be done independently of bilinear filtering (e.g. GL_NEAREST_MIPMAP_LINEAR) and plenty of games support it but I guess TF2 might not be one of them. Somebody please correct me if I'm wrong.

those lines are the texture mip levels changing
mat_mipmaptextures 0 fixes it, but things in the distance look pretty horrendous