It all comes down to trust.
If the agreement is to not cheat then obviously don't cheat. If someone cheated on me when we decided to not be open, then I wouldn't be able to trust them anymore. Thus although I might still stay with them, I wouldn't be able to justify that we have the most trusting relationship in that aspect. And they would certainly tempt me to push for a more open relationship with regards to sex.
TLDR: Its inexcusable trust wise but compromises can be made.