Moral realism fallacy alert?

If at some point most people believe that killing mammals for food is monstrous, and it is banned, and children learn with horror about 21st century practices of murdering and devouring millions of cows and pigs each year, will that make it wrong to eat a hamburger now?

Yes, that will make it wrong in their view. There's no law of nature that says different people from different times should have identical moral judgements.

I certainly don't feel that the moral value of my actions should depend on the beliefs of people living hundreds of years in the future.

No, the moral value of your actions in your view doesn't have to depend on their beliefs. There's no law of nature that says different people from different times should have identical moral judgements.