I'm not quite sure if this is the best place to post but I'll ask anyway.
I recently started playing on FTE and I noticed the skins textures appear off. This happens to online players aswell

That seems weird, is that using FTE and just the pak0/pak1.pak?

Yes. I put FTE quake into my main quake directory which is what was recommended

Where did you get your Quake directory from? Steam?

No My quake is from GOG

Actually I believe I found the root of the issue. On FTE I am using the software mode and it warped the player textures, am I able to turn something off so I get the proper player textures and keep most of the software option on?

Hmm, I'd go on the QuakeWorld Discord and ask in the #dev-corner channel, maybe someone knows there. Or maybe Spike (FTE Developer) is around.

Also try in a fresh directory with just fteqw.exe, id1/pak0.pak and id1/pak1.pak