Have you explained to them why?
I'd be tempted to remind them that it's their workplace and to grow up!
I can understand you not wanting to ruffle feathers though, at the end of the day, you are there to manage and not pander to all their personal preferences, especialy if it gets in the way of work efficiency.
Are you sure there isn't a specific reason for someone not wanting to move? Might be worth a private chat to make sure there is no element of bullying or nastiness of similar going on which is why there has been the reaction there has.
If you can compromise in a way that doesn't undermine your authority but keeps the peace then go for it but you can't please everyone all of the time and they are there to work, not socialise.
Be reasonable but not a walkover, if you give in now without good reason then you could be making a road for your own back.