I mean I see both sides.
On the one hand, from a football spending perspective, cap spending is all that matters. So, from a cap perspective, its kind of hard to justify letting him go, unless there's a significant player you would want to spend that money on. Given we will likely have space to spend if we need it and that any FA signings at this point are largely of the "bargain" variety, that's likely not an issue.
On the other hand, as a business owner, paying $6.5M to a guy who ideally won't even play for you is a tough expense to swallow... especially when you have the option of not paying him. In the grand scheme of things, probably just a drop in the bucket for the organization, so that's probably not a factor.
There's also, in theory, something to be said for if Stanley wins the job outright, not having to look over his shoulder at what would easily be the best backup LT in the league. If he wins that job, the FO could show extreme confidence and support in him by cutting the high paid guy he just beat out.
Ultimately, I think he stays, but the only scenario that surprises me is Stanley not being a starter at some position. Monroe being cut, traded, benched, or even the starting LT for 16 games wouldn't surprise me in the slightest.
I think it is going to be tough for Stanley to beat out Monroe (unless Monroe is MIA like last year). Don't get me wrong I would love to see Stanley starting over Monroe, but it is rare for a rookie LT to come in and play at a high level.