One of the answers states that If a Cohen marries a divorcee, he remains a Cohen but is deprived of Cohen privileges and should not get a first Aliya (Shulchan Aruch EH6; ibid OC 128,40). But, in my orthodox shule, my Rabbi refuses to give this Cohen any Aliyot except for one day a year when he has yarzheit. Is this right?

There is no simple answer to your question, since the degree of leniency or strictness on questions of social sactions depends to a great extent on the nature of the community and the effect such a sanction will arouse. Obviously, the Rabbi is trying to emphasize the severity of straying from halachic norms. Alot depends on the question if this is an isolated case, and how the sanctions would work with other aveirot. I don't know any reason to single out this aveirah for more stringent sanctions than another. Certainly the person to answer these questions is you Rabbi himself and I suggest you ask his sources and logic, with respect and recognition of his authority in such a matter. The worst thing to do is to denigrate the Rabbi behind his back.