They wouldn’t have bombed Pearl Harbor and we might not have gone to war....
The JAPS bombed Pearl Harbor, not the Germans.
Hitler never did have much of a hope of capturing and holding the Caucasus oil fields - they were in flames when his leading troops finally got there and it would have taken at least a year to put them back into production in the face of vastly superior forces. So stabilizing a defensive line on the Volga was out, hence Stalingrad served only as a holding action while Army Group A was extracted, rather than the anchor of a defense as Hitler had visualized. Plenty of his generals had warned him.
Kennedy, the fellow who deployed troops to Vietnam, might not have been replaced by LBJ, who increased them. Jackie might not have married Onassis. We might still be able to mail-order rifles. Heck, who knows?
Reconstruction would certainly have looked different under Lincoln than under Johnson, but beyond that, it's impossible to say. The main point of the thing was that Our American Cousin wasn't a very good play and I doubt if Mrs. Lincoln would have had a nice evening anyway.
As for GHWB, it's hard to decide. If his replacement were conservative in the sense that he wouldn't have led a war over Saddam's occupation of Kuwait, then we may well have had to fight for the possession of the Saudi oil fields, a rather messier proposition. Or not, depending on whether or not Saddam would have kept coming, but there wasn't a lot to stop him at the time. He did, however, couch the affair in strictly internationalist / collective defense terms that we've been laboring under since. This one is as much speculation as the others.
I'll pose a question in reply: what would have happened if Frazee hadn't wanted to put on a play named "No No Nanette" and kept that punk kid pitcher named "Babe" in Boston?