FaceBook Friends with Ex-BFs/GFs?

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If a woman/man is FaceBook Friends with former boyfriends/girlfriends, should that bother the current boyfriend/girlfriend?

Would such ongoing FB friendship slow one down in thinking about marriage?

To be clear: Yes, the FB friends in question were sexually involved at one time, but no, they are not now, and I don't anyone is worried about cheating.

Current BF/GF has asked that woman/man de-friend such person, but woman/man finds that controlling and shows lack of trust.

Current BF/GF just wonders why, if woman/man wants to really get serious, why she/he isn't willing to "forsake all others"? It's bothersome, a thorn in the side of the relationship.

Woman/man says to defriend would cause a big awkward situation amongst their mutual set of friends.

Current BF/GF does not want to be controlling, has gently mentioned it 2-3 times over the course of 2-3 months, has gotten polite resistance. Current BF/GF doesn't want to twist any arms into submission on this, but doesn't find this to be long-term acceptable either