This reminds me of when people complain about a lack “freedom of speech” but what they actually want is freedom from the consequences of their speech.

Plenty of jobs come with personal life restrictions. Work nights. Work on an oil rig. Work on an aircraft carrier in the ocean for months at a time. Everyone is free to not take those jobs. I don’t see why a “no affairs” clause for a CEO should be all that different. If you don’t consent to the rules, take a different job.