They can try, but if they tried to fire a player or heavily fine them, it could be contested I would say.  In a court of law, "should" does not hold any water as being a word meaning its required.

Also, in doing a little more research on this, I found out that the provision I listed above isnt even in the 2017 NFL rules book...AT ALL.  In fact nowhere in the entire rulebook is "anthem", "flag", or "stand" (in reference to the American flag/National anthem) mentioned in any way.  The closest it gets talks about players not wearing decals or images that are not preapproved by the NFL while that player is on national TV.  

Link to 2017 rules:  http://operations.nfl.com/media/2646/2017-playing-rules.pdf

So, after reading that - no, I dont think that the owners or even the NFL have the right or even the discretion to impose any form of consequence related to not standing for, or even being on the field during, the anthem.