The world would look the same way it does now with or without objective morality. Objective morality is just the idea that moral truths exist independent of individual beliefs. E.g., that raping babies is an inherently immoral thing regardless of an individual’s feelings about it
Again though, I personally don’t believe this. I just won’t claim to know that there is no objective morality. No one can know that, the same way no one can know that there’s no god, or anything else unfalsifiable
The best argument I’ve heard for it, from a moral philosophy professor and personal friend of mine, is (paraphrasing) “I know for a fact that genocide is inherently wrong, and I’m not open to debating that. It’s just true.”
People before gravity was well defined:

I’m an amoralist and a determinist; I only disagree with you on the basis of claiming these things as fact