Intolerance of anti-black people makes you intolerant,not tolerance of black people. That intolerance would be fine(I certainly don't tolerate anti-black people in my personal life) but I would want to make every effort to be professional and respectful towards a skinhead at work.
I do not intend to have a Philosophy 101-level debate here, but would like to say that some things are not morally ambiguous. It is fine and good to be disrespectful towards skinheads at work, on the bus, or anywhere else. It is not fine or good to be respectful towards skinheads. Someone who wishes violence against a class of people based on their race does not have a place in a well-functioning society for these beliefs to be openly tolerated and accepted.
I presume you would only complain about the workplace behaviour of this skinhead.
If your target skinhead kept all his skinhead behaviour out of the workplace, and only displayed respect and tolerance to his colleagues, would you still organise to get him fired?
To be clear skinhead is sort of ambiguous. I'm reading neonazi and I think you meant neonazi but people do actually use the term to mean other things it seems.
If you mean neonazi I would for no reason I can imagine tolerate them. Would you tolerate someone who hated and wanted to subjugate or murder some portion of your loved ones because they were polite at work so they could earn a living?