I am no prude by far. But I have been in this situation as well, in a secure loving relationship ( or so I thought at the time). Needless to say it did not end well. It turned my man into a total control freak, trust was gone. He accused me of seeing people on the side. He wouldn't let me leave his sight. It was a crazy situation.
I would say go with YOUR gut on this.If this is the man you plan to marry think about the fact that in the future he may not want a woman willing to sleep with other men as the mother of his children. When I got pregnant with my ex husband's child my entire pregnancy consisted of him calling me a prostitute in public constantly and swearing that I was pregnant by another man. He even told his family that I constantly cheated on him, leaving out the part where he was THERE.
After our daughter was born and with concrete proof that she was indeed his child he would have NOTHING to do with her. We divorced 8 months after her birth.
To this very day, in his head, I was a cheater. He actually told our daughter that he left me because I was a prostitute who constantly cheated on him when we were married. When in fact I slept with 1 guy, his choice, while he was in the room, one time. My gut told me no but after constant begging I caved in. When I look back I often wonder if things would have been different had I maintained my original answer.