I don't think that government employees hold any special privilege in terms of private contracts, but I don't know. At the very least, it would be interesting to find out.
I know that recently there have been some gun shops that have been refusing to serve government employees, so there is at least a small amount of precedent.
Would a ToS hold up in court that specifically denied access to the company's service by government employees?
If a company had that in their ToS, and they discovered that a government employee had used their service, could they sue for damages?
Are businesses in the US obligated to provide service to government employees?