You say you do trust her, but I think you don't completely trust her and you don't like the fact that she identifies as poly. Whether you're in a closed or open relationship, there WILL be people who approach your partner. That's just life. It will happen. Some of them will be honourable, some of them won't. YOU CANNOT CONTROL THAT. I think that your feeling upset is about the fact that you would like to control those people and their actions. YOU CANNOT. You need to accept that fact first. Then, you need to figure out whether you really do trust your partner.
My personal experience: I have a partner who is poly and meets a ton of people who are interested in her. Some of them would prefer that she be primary with them and not me. I trust her to tell me what's happening and I trust her commitment to me. If she chooses to leave me to be with them? Well, that'll be her decision. I CANNOT CONTROL WHAT SHE DOES AND DOES NOT DO AND WHAT OTHERS DO TOWARDS HER. I'd hate to lose her but I am secure in the fact that I probably won't and that if I do, I will survive.
STOP LOOKING AT OTHER PEOPLE: you're projecting your lack of trust and self-confidence onto others. Look at yourself, your partner and the trust in your relationship. Really look - no excuses, no denial.
My personal experience: I have a partner who is poly and meets a ton of people who are interested in her. Some of them would prefer that she be primary with them and not me. I trust her to tell me what's happening and I trust her commitment to me. If she chooses to leave me to be with them? Well, that'll be her decision. I CANNOT CONTROL WHAT SHE DOES AND DOES NOT DO AND WHAT OTHERS DO TOWARDS HER. I'd hate to lose her but I am secure in the fact that I probably won't and that if I do, I will survive.
STOP LOOKING AT OTHER PEOPLE: you're projecting your lack of trust and self-confidence onto others. Look at yourself, your partner and the trust in your relationship. Really look - no excuses, no denial.