Yes, it varies by profession and violating the unwritten rules for your profession can be seen as either unprofessional or pretentious.
One basic rule is that you do not put a credential on your card twice. You don't write Dr. John Smith, MD. You're either Dr. John Smith or John Smith, MD. You don't put Jane Smith, JD, Attorney at Law. You're either Jane Smith, JD or (almost always in the case of an attorney) Jane Smith, Attorney.
The other rule is that you don't put credentials on your card which are not relevant to the business being presented by that card. So, if Jane Smith is both an Attorney and a CPA, well those are related credentials and she can and should put both. But, if John Smith is both an MD and a CPA, it's gonna depend on what his business is. If he's got a family medical practice and does taxes on the side, well those both separate businesses and he's gonna need two cards. But, if he works as a financial consultant for doctors, he might put both on his card.
The other general rule is to list only the highest-level qualification you have. So, Bob Brown, Ph.D., M.S., B.S. may seem impressive, but it's inappropriate. A Ph.D. implies a Master's and a Bachelor's degree or equivilent. So, it's proper to say just Bob Brown, Ph.D.
If you have two equivilent-level degrees, it depends on your business. For example, Doris Brown, MD, JD. If she has left law and is practicing just as a doctor, then she should leave off the JD. If she's given up medicine and is persuing a legal career, then she should drop the MD. But, if her legal career is specialized in medical malpractice, then both may be appropriate.
A person with two unrelated and independently-earned credentials, that person faces a similar situation. Albert Johnson, CPA, MFA. If he's working as an art dealer, then be MFA and leave the CPA off. If he's working as an accountant, then be CPA and leave the MFA off. If he's got two separate businesses going on, then separate cards are required. Only if he has combined the two into one practice, accounting for art patrons or Chief Financial Officer for an art museum, some such thing, should he list both.