There are many things a president may do or say which would render them a bad president but not illegitimate. There are also, indeed, many things a president may do or say which would delegitimize their presidency entirely. We need to get to the bottom of the difference.
If a president says that soldiers who get caught and tortured by the enemy during war are 'losers', that is certainly reprehensible; however, that is the president's opinion. Nothing illegal or unconstitutional happened. A president declaring that the color orange will henceforth be the official color of the White House, as opposed to white, in order to invite attention to his masterful hair and divert attention from all the white guys ... that would be bizarre and inappropriate, but not disqualifying. He could even rename it 'The Orange House', or, as I suspect, something with 'Trump' in it, and still he would not be an illegitimate president, only a bad one, an embarrassing one.
What if Trump, while she is at the podium speaking, walks up from behind an attractive female foreign dignitary and starts grinding her from behind, then he is seen reaching around and grabbing her by the pussy? She screams out in objection, but he only spanks her and laughs. It's all on camera.
First of all, anybody who thinks such a scenario is an impossibility has not been paying attention. In fact, I would not be surprised if film already exists showing Trump doing things similar to what I have just described. Many farcical things have happened lately.
But would that be disqualifying? Yes. Why? What I have described is sexual assault - it is blatantly illegal. Not only that, it is flouting the law. Doing it publicly, feeling that the law does not apply makes it an aggravated and intentional thing. And even though prominent Republicans would look their daughters in the eye and say, "America knew that Trump is a pussy-grabber. Voters understood when they voted for Trump that he is a man's man who will grab some pussy from time to time." ... they will not be able to undo the sheer illegality of the act.
As an aside, but pertinently, to channel Nixon and declare that being the president means one is not capable of breaking the law ... is also, all by itself, a disqualifying sentiment.
There are things which can be said and done which are in bad taste, even bigoted. But other things are illegal, as well as immoral, or they are blatantly unconstitutional. We must watch that line or risk losing everything.
How about allowing a hostile foreign power to sabotage our elections - our basic right of vote - without any repercussions? How about, indeed, saying how the hostile foreign power who sabotaged our last election - did I mention that is our right to vote being sabotaged? - has a great leader whom we should embrace? Isn't that treasonous and disqualifying?
Yes.