Can a pilonidal cyst cause low platelet and neutrophil count? mass production of antibodies also attacking my platelets? similar to what hiv does?

Doubtful: The cyst it's self would not cause any lab abnormalities. If it got infected you would expect it to raise your WBC's, not lower them.

Pilonidal cyst: A pilonidal cyst should not cause a drop in platelets or a drop in the neutrophil count. If that occurred, I would look for another disease process that could account for that. Pilonidal cysts can become infected - and if someone is very ill from that, you might see derangements in blood cell parameters. Those infections involve bacteria, and therefore are very different from HIV related effects.