Tenured professor’s husband convicted of a drugs-trafficking felony – are there any career implications?
This is a question which can only the respective university can answer. (I assume in my answer that the police has not proven involvement of the professor in the drug thing.)

Ideally (and most likely also by law, but you do not specify your location), husband and wife (or husband and husband, wife and wife) are treated as two separate people -- if one does a crime, it does not mean that both are involved. That the professor is not involved should also be the default assumption of the university unless the police proved otherwise.

Of course, people often talk and make decisions which are not backed up by the law. It may be of course that there are implications for the professor -- most likely, it's not explicitly said that they are connected to the drug thing.

For implications outside of the university, the same holds. Ideally, nobody treats the prof differently, but people sometimes do.