I asked about this in the comments section of another question, but no one responded, so I guess I'll ask it here. The question involved expressing that someone was both a movie star and a politician, and various good alternatives were offered. It occurred to me that 兼 might work, so I checked example sentences in a dictionary, and found 「総理大臣兼外務大臣」. That seems similar enough. However, I was wondering, does 兼 work with two things as wildly disparate as "movie star", and "politician", or does it sound strange? In other words, would one expect a stronger or more logical connection between the things that 兼 connects?
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ALC samples suggest that you do not want to mix movie star with politician:
Most samples come from newspapers, having a quite formal flavour. It clearly shows that you want to link occupations (rather than favourite pastry), and that they have to be related.
My suggestion would be to do some research on Arnold Schwartzenegger and Ronald Reagan, and in doubt, to avoid using 兼 as in the title of your question :)
Although describing 映画スター兼政治家 as “weird” might be too strong, you are right that 兼 is more often used when the combination has a close logical relation.
In my understanding, this is because 兼 makes a compound word and using a compound word implies that the speaker considers the combination as a single notion. Using an example from Axioplase’s answer, it is reasonable to consider ロックギタリストでもあり歌手でもある人 (a person who is a rock guitarist and a singer at the same time) as a single notion, so calling such a person ロックギタリスト兼歌手 makes sense. On the other hand, it is probably uncommon to consider 映画スターでもあり政治家でもある人 (a person who is a movie star and a politician) as a single notion because being a movie star and being a politician seem very different, and therefore 映画スター兼政治家 sounds a little off.