My particular case of arthritis doesn't give me any trouble with the C major chord; for me, it's the first-position A major chord ~ which I used to make easily with one finger ~ that gives me problems. It's almost impossible for me to play this chord without muting the open high-E string. (I believe that this is the same note on the same string that poses problems for other folks with the C chord.)

The problem is that my fingers no longer bend backwards at the top knuckle ~ neither the index (with which I used to hold down three strings to play the A) nor the pinky (used for the same three strings in the same "shape" but in barre-chord form, that is, Bb, B, C, and so on up the neck).

For the A, I try to "fudge it" by playing the simplest form of the A7 (002020), muting the G string with one finger but being careful NOT to mute the high E. And as far as the barre chords like Bb, I just can't play 'em at all.

On the other hand, I'm actually regaining some ability to play the top two strings with my semi-crippled pinky. I can't move it as fluidly as I used to, but I'm learning to adapt and to hit the same notes as before, but in a more stolid and deliberate manner.