Conserved proteins are non immunogenic
Immunogenicity is


  the ability of a particular substance, such as an antigen or epitope, to provoke an immune response in the body of a human or animal. In other words, immunogenecity is the ability to induce a humoral or/and cell mediated immune response.


If a protein is highly conserved between species it means that its epitopes will be recognised as self by most species, hence the organism will avoid producing antibodies against them to prevent autoimmunity.

You may want to read about central tolerance to see how T cells and B cells are rendered non-reactive to self.