If this is someone I really intend to hang out with and they’re having a private text conversation with someone the whole time, I would consider it rude. It shows that they’re not fully interested in spending time with me and find their text conversation important enough to have it the entire time they’re with me (this has happened to me before). I don’t mind if someone texts someone a few times while they’re with me, I do that too. If someone texts me while I’m with someone, I’m not going to ignore them, but I wouldn’t instigate a full-blown lengthy conversation with them.
It’s like when I was giving my presentation in Economics class and my (boy)friend Rory was texting on his iPhone beneath the desk while I was beginning and I was like “Rory, stop texting” in front of the whole class and everyone looked at him and he turned red in the face. I felt kinda bad about embarrassing him, but he told me later that he thought it was funny. If my teacher wasn’t going to get people’s attention, I was.
Unless the conversation is very important, then I don’t think a person should be doing that when they’re spending time with other people. I try to give the tangible people I’m with my full attention.