Legally, yes. I mean it still depends on a lot of things but mostly at will employment contracts will have clauses about such things. You will have to get approval from legal before you can get on a board of even a dog rescue or a glove repair company. A practical consideration is simple like if you are a google exec and you are on board of a dog rescue company and that company gets hit with allgeations that you are just shooting all the dogs and selling their meat to some foreign nation. News will cover it as "Google Exec on Board of Evil Dog Rescue Company" so you extend that repuation risk to Google as well since you are actively employed there. Obviously an extereme example but that's the kind of logic they think of.

Morals imo often have nothing to do with law, but fairness does.