JB is one of those " bollocks to what they think, I don't care il make my own mind up brigade" I'm sure though he did see June and nevill as his natural parents though and vice versa as a natural son. He'd been with them all his life.
The " bastard" jibes at greashams may have upset him, but I don't think it effected him his adoptive status as he matured
Did his natural parents reject him pre massacre for any meet ups?
I have read Jeremy wasn't interested in meeting them prior massacre
I understand him to have made contact with his birth parents around the same time that Sheila made contact with her mother -might this suggest they both experienced mutual 'difficulties' with their adopted parents?- but whilst Sheila's mother welcomed the contact, JB's parents rejected his. I can fully understand why he'd have said he had no interest in contacting them. A mix of hurt, and pride.
I think Nevill had less problem with accepting J and S as his 'own' children, than June. I don't think she ever got over her inability to conceive -although such may not have been her fault, of course- and because of her very religious convictions, would have believed God was punishing her. Hence her desire to make her tainted (illegitimate) children, perfect.