I am not misunderstanding the situation. If you omit me from a group message with our circle of friends because of the color of my speech bubble, you are not a real friend. Full stop.
I don't know you, of course we're not friends. I addressed this in my comment. There are group chats you are part of and ones you won't be part of. Most people maintain multiple different overlapping group chats.
Just the phrase "blue bubble friends" strikes me as absolutely wild, foreign and ridiculous. But, I admit to being almost 50.