If the full set of pronouns is "judy", standing in for he/him/his/himself, I'd think it has the potential to become quite confusing.
If you see Mac, could you please ask judy if judy can stop by my office and bring judy books with judy? I don't need anyone else's books, just judy - but I need judy to bring them judy.
If this becomes normalised, I suspect English will evolve similarly to languages like Korean where it's standard to just use the name every time - or to skip pronouns completely if the meaning isn't ambiguous.
(Also, Apple autocorrect insists on making "judy" into "Judy", so there's a microaggression waiting to happen).