There are two issues here.
1) Whether his comment was racist.
From what you've said OP it doesn't sound like it was, the Oxford dictionary definition of racist is
Prejudice, discrimination, or antagonism directed against someone of a different race based on the belief that one's own race is superior.
Simply stating that a group of travellers have left a local park in a mess doesn't meet that definition.......
Based on the limited info you've given imo his employer are incorrect to call him racist.
2) Whether he has behaved in line with his company social media policy.
If his company don't have a social media policy which they can prove that he has been made aware of (this is key) then there is not a thing they can do.
They might try to say that he has "brought the company into disrepute" but for this to stand they would have to be able to show that it is clear from his Facebook profile that he works for them, so if he's listed his employer, posted previous statuses naming them or posted photos of himself in work uniform etc.
If they have a policy and he has been made aware of it then it comes down to what that policy says. Usually they have things around posting anything political, racial or discriminatory. It is possible that what he's posted, taken in the context of other posts/comments from other people linked to his would contravene their policy in which case they CAN discipline him.
They do have to follow proper process though and that certainly DOES NOT involve just getting him into an office and demanding that he signs a confession!!!