I think June and Neville were (without any disrespect meant) 'products of their time' in that my Grandparents would have been the same age, they didn't particularly show open affection and lived in a certain way, you did what your parents told you, you were good at school and church, you left school and went in the forces or had a job, then you got married, had children and taught them the same and my Nan can't (even now) understand that people don't get married of sometimes divorce, have sex outside a marriage (even though she HAD (!!) to get married) and might not have a job etc-in other words the world is changing and while they stay the same, Neville reminds me of my Granddad in that he probably just accepted things and didn't want a fight, June probably wasn't backwards at coming forward which probably caused more hassle than it solved and she probably told Sheila off because of her lifestyle and tried to put the fear of God into her, not realising it wouldn't achieve anything and make things worse.
I don't think the issue is about the children being adopted, I think June and Neville treated Sheila and Jeremy the same as they would have been their own but I think when you find out that your adopted, you have a curiosity of perhaps wanting to know what your birth family would have been like.
I have 2 half brothers who were adopted out and whilst I have always known one and we have a good relationship with as much as if we'd grown up together, I know who the other is and have not met him and I have no desire to do so, I have said by all mean don't make out I don't exist but I don't want direct contact with him at this time, it's just a personal preference for me and I don't know what either my sister or half brother think-if anything. I also maintain a good relationship with my brothers' half sister and brother.