Well, my fursona Jau has two major forms, the little dragon from only wearing a vest and bracelet and his fully dressed human form.

And honestly, he doesn't really feel awkward around other furries in either form if they wear more or less than them because, Jau's used to being a little dragon who doesn't wear much in a world of fully dressed humans.

If he saw a naked human and was a little dragon, then it'd get awkward because he expects humans to be fully dressed in social occasions but isn't wearing much himself.

Eddie Bear and Dan D Lion would feel extremely awkward without their clothes. They make their character complete, and they both are partial fursuits!
Shaemus MacDuff went without his kilt once. He felt very awkward.
Fu Manchu and SabreKatz run around naked. They're awesome like that..

As for how they feel around others, clothed or not, there's not an ounce of concern. It's how they are.
They all do have an opinion on the choice of clothing that some furs wear, but I'm not going there.