If I went actively looking for people on social media who have posted racist things whilst having their employer's details on the profile, I recon I could find easily over 200 on any given day. I wouldn't do it because I don't particularly care about what a random lad from Scunthorpe thinks about non-whites, but it's clear from
@VeevaVee 's post why he does and it's fully understandable. I think the real question is what does he hope to achieve by reporting these people with racist views? If this person is sacked then it would almost certainly make him resentful and more likely to harden his (and potentially his family/friends/colleagues) racist views. Having known someone who got sacked for racist behavior on social media, I can say at least for him it made him far more bitter against both minorities and 'liberals'. On the other hand you've also got to consider the detrimental impact on those people under him that he potentially might discriminate against. If there's any evidence that he has been mistreating his non-white colleagues then he deserves a sacking. If not then a warning and attending one of those courses aimed at tackling and educating workers on racism would be more appropriate.
My answer on how appropriate it is to report someone for this is based on the response of the employer so I'm just going to sit on the fence and say I don't know. Ultimately I think it should be up to the employers to monitor their worker's social media pages if they have the employers details on them for this sort of thing. If
@VeevaVee had found a random person and then through extensive stalking found his employers details then I'd have a different view, which I know is kind of contradictory given that my answer has been based on this person's conduct in the workplace and not on the wider issue of freedom of thought.