First as a culture or society we need to redefine these words and stop using them incorrectly.

Monogamy is not a realistic idea; we are animals and as such have different things that drive us.
Loyalty is a relationship can happen even if one or both are having sex outside of the relationship.
Honesty and commitment are more important.

Your heart (Love) can belong to one yet you can have sex and other feelings (Lust) for another.

With all the other problems in the world why focus on this?
The idea is to find someone that has your set of ideas (not necessarily the word Morals as that is something different).

Find a relationship that workds, stay honest and life live with less stress, if not then why bother?