> The clash that occurred would have been hard to prevent whenever it happened. As others have pointed out, even basic biology (immunity) was different enough to make an enormous difference without people consciously having to do anything.

In the 16th to 19th centuries, I suppose it would have been an insurmountable medical problem. But what if they were separated until today? Perhaps in an alternate universe, instead of a wooden sailing ship to cross the Atlantic Ocean, toxic gas bubbled up from the mid-Atlantic ridge (and a similar barrier in the Pacific), requiring pressurized aircraft to fly over. Or the two groups were on separate planets, requiring space travel to meet.

Would we be able to deal with the medical problems today?

Or, in a less unlikely scenario, there were plagues in the Americas that decimated European settlers more than the reverse, allowing the Native Americans to co-opt European shipbuilding and colonize Africa and Eurasia. Interesting to think about!