Hawkeye... I want PICTURES! I want to see you in your umpire uniform with jewelry hanging from wherever and blond dreads! Did you have an adjustable cap for your pony tail to hang out?
SRW... you won't find any RULES regarding umpire body adornments. It is a matter, as Hawkeye says, of professional appearance; of being taken seriously. It is more the total package than a technical boundary of 0, 1, 2, ... items.
You won't find a rule about wearing a watch, either. Have you ever been told by a UIC or clinician not to wear one?
And, since it is a matter of appearance, yes, there is a difference between female and male professional appearance in our society.
JMO.