In an article on his blog, Piercarlo Valdesolo, one of the authors of the book “Out of Character”, which I’ve quoted before, writes about an interesting experiment:
Forbidding Makes the Heart Grow Fonder | Psychology Today
The essence of which is that jealous behaviour and putting limits on your partner will only make him (or her, there were no gender differences) think about the forbidden fruits even more and even become more willing to cheat.
So even if you insist on monogamy, a relaxed attitude makes it more likely that your relationship reality comes close to your ideal.