If an engaged person is regularly looking up someone they casually dated years ago on social media without contacting them, is that a red flag?

My fiancee is still regularly looking up a girl that he dated years ago. I told him how I felt about it, yet he still does it. I feel like you can't look up someone you aren't thinking about. He says he's not thinking about her. He's just nosy. Either way, I'm becoming indifferent to the whole situation and I'm losing interest in him. I'm thinking about ending the relationship. I can't marry someone that is stuck on someone else, but I'm just curious... how would you ladies feel in this situation. Would you care?

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