First off, a conversation takes two people. There's also a difference between someone simply being polite and being engaging. There's also a difference in respectful behavior and disrespectful behavior. Depending on how these ingredients are mixed, it could be nothing or something of concern.
For example:
You step away for a moment, a stranger comes over and engages your girl in small talk. She's being polite, but not engaging. You come back, she introduces you. The guy realizes she is there with you and disengages from the situation.
The above is the most respectful situation amongst all involved.
Another example:
A guy approaches your girl while you're in the middle of a conversation. She starts talking to him, becomes more engaging. She never introduces you and begins ignoring you.
That's a very disrespectful situation for both the girl and other dude. I would place most of the disrespect on the girl though.
Yet another example:
You step away for a moment and come back to see your girl in a convo with another guy. She introduces you and the guy still hangs around. You can tell your girl is becoming increasingly uncomfortable being polite to the other guy. He then starts touching her arm and she gives you a look of being uncomfortable.
In this case, the guy is being disrespectful.
Final example!
Your girl ignores you, starts opening on other guys in your presence. The other guys seem weirded out she's doing this in front of her boyfriend.
She's being disrespectful, but the other guys are being polite in the convo.
In all of the above, I think there's only one of those situations where you could go after the guy. There are multiple situations where the girl would be who should be addressed.
In reality, if your girl is receptive to chatting up with guys and/or getting their numbers... better to know that sooner than later and treat her accordingly. I think for a girl that is in to you, that shit just isn't happening. In the cases where the girl is in to you, you should be more concerned about those she is in frequent contact with (school, work, friend groups) versus random strangers.
For example:
You step away for a moment, a stranger comes over and engages your girl in small talk. She's being polite, but not engaging. You come back, she introduces you. The guy realizes she is there with you and disengages from the situation.
The above is the most respectful situation amongst all involved.
Another example:
A guy approaches your girl while you're in the middle of a conversation. She starts talking to him, becomes more engaging. She never introduces you and begins ignoring you.
That's a very disrespectful situation for both the girl and other dude. I would place most of the disrespect on the girl though.
Yet another example:
You step away for a moment and come back to see your girl in a convo with another guy. She introduces you and the guy still hangs around. You can tell your girl is becoming increasingly uncomfortable being polite to the other guy. He then starts touching her arm and she gives you a look of being uncomfortable.
In this case, the guy is being disrespectful.
Final example!
Your girl ignores you, starts opening on other guys in your presence. The other guys seem weirded out she's doing this in front of her boyfriend.
She's being disrespectful, but the other guys are being polite in the convo.
In all of the above, I think there's only one of those situations where you could go after the guy. There are multiple situations where the girl would be who should be addressed.
In reality, if your girl is receptive to chatting up with guys and/or getting their numbers... better to know that sooner than later and treat her accordingly. I think for a girl that is in to you, that shit just isn't happening. In the cases where the girl is in to you, you should be more concerned about those she is in frequent contact with (school, work, friend groups) versus random strangers.