I just have to say
I have never heard of anything like this coming from an LGLO! I am very upset by this! For one thing, I know that many LGLOs (including mine) will not accept anyone who is a fully initiated member of any other GLO (with the exception of honor societies), so I'm not sure who is even allowed to do this according to national policy. Second, I think it is pathetic, and I'm sorry to hear that it has happened to people. I don't understand who would be that "hard up" for members that they would try and get someone who is already happy in another organization to join theirs. Even if they were able to somehow persuade someone to disaffiliate, would they really want to be someone's second choice?
ETA: Regarding the "traitor" issue-- I actually experienced this in "reverse" so-to-speak when I was an active. There were Latinas who had joined NPC organizations who would give us dirty looks in the library when we were studying, and they would start rumors about us. I never understood why because we didn't even know those women and had never even spoken to them. Either way, it is wrong, and no one should be criticizing another person's choice of organization, as it is a deeply personal choice.