Shopping613 I agree very much with the idea that it’s important to want to improve.
However I don’t see the point in saying that one person is a real jew (wants to get to a higher level) and the other is not.
First of all, this hardly help you at all with your own torah and mitvot. That we are expacted to respect every person is for sure. What’s the point then of saying that one person is real and the other is fake?
And secondly you can’t really know who wants to get better and who doesn’t. People could be making progress in ways you’re not aware of. Also some people might have been Bney Alyia when they were young and lost it with the years. They may get back on their feet at a later point. You can’t really label them as anything.