Your question isn't worded very clearly, but I'll take a stab. Just because someone is in a polyamorous relationship does not mean he or she does not care whether their partner has sex with other people; even if they do not mind. Being okay and accepting of it doesn't necessarily negate the caring or protectiveness toward their partner.
But everyone will show that caring in different ways. It seems that many couples will usually establish some sort of guidelines to make sure their partners are safe, whether that is requiring frequent text messages during the date, complete knowledge of where they will be and with whom, or even accompanying them on first dates to meet the person.
So, what does your girlfriend mean when she says she "would be concerned about the protection feelings of a man towards his girlfriend if he didn't mind her sleeping with other men?" Is she afraid you will stop caring about her if she does have another partner? Or is she afraid you will be overprotective and start trouble? Remember, polyamory is not just about sex; it is about having multiple loving relationships. If she has such concerns, it would seem best of she tried to establish a good rapport and caring relationship before getting sexual with someone else.