When was the last time a President won, where the other side didn’t call the election “illegitimate”?

As someone else, said, not like we've had in 2020.  There's been longstanding Republican memes that Democrats win through fraud.  But that was largely on the fringes.  It was never given official legitimacy by the party leadership or by a losing candidate.  2020 was different.  Trump began saying that the election would be stolen before it was even over.  Then he began claiming, against all evidence, that it had been stolen when he lost.  You didn't see that before.  You didn't see Mitt Romney, or John McCain, or Bob Dole, or George Bush saying that the election had been stolen. 

To the extent of 2020, never in my memory.

There was always be someone who is unhappy to some extent, especially when the popular vote didn't prevail, but few that called an election illegitimate, and persisted in doing so.

I don't remember anyone challenging Obama. Maybe I'm wrong, I just don't remember anyone doing it.  Trump was the last one, and he's right, that's the rub. I saw it happen, and then I saw what happened on both sides afterwards. Now the tide has changed. The censorship and self-censorship of news media about the 2020 election is still gong on, so the only people who are paying attention are looking at various sites including YouTube to see what is current about the fraud. YouTube is trying to screw with searches about it, and are censoring some of the videos about it, but not all of them. 

Al Gore was the one before that, at least concerning presidential elections. And from what I remember, he got treated fairly. Trump didn't get treated fairly, and it won't be long before people just cannot ignore it anymore.