I'm not sure i see the problem guys.
A capt flying on the right seat has to be right seat checked at opc/lpc. flying is not allowed on the line (normal ops) just radio and panel management, which on a 737 is not rocket science.
As for crm, lets not hide behind it. good crm is not a fixed entity, you create it on the day. me thinks its a bruised ego in some cases or resentment about doing a lca on a fri night in the right seat, and having to suffer someone elses techniques.
This is where your professionalism we hear so much about on these forums should come into play and create a good atmosphere that is conducive to and allows good crm to develop.
its only a safety isue if you cant deal with it. skills wise its not a challenge so there must be another hurdle creating any problems.see above.
I've been doing co capt in various firs for years and only here in the uk do I hear the dislike of it being hidden behind crm and safety. sure its a pain but you are a professional. deal with it on the day and try and get a policy change in the long term