Gilozard: ...In the US, no one can stop anyone from running for office. We always start out with a field of crazies and it gets winnowed down. Trump has run for several positions but it never goes anywhere.
The only change this time is that the media is giving him, and all the nutjobs, more air time than usual.
Trilarion: Not only the media. For example while Donald Trump has the right to run for office he is not entitled to make it under the banner of the GOP. He could run as an independent after being excluded from the GOP for having incompatible views. Or the law prosecutors could accuse him of hate speech and discrimination (for example when asking for marking people of a certain faith) and sentence him. Or people instead of enjoying the show could publicly express their distaste for him and put more pressure on the media and their local GOP representatives to end it at least now. WIthout it it seems like he has at least some support in the GOP and among the voters and given his dangerous ideas I think this impression really should be avoided.
I wouldn't mind if he would be a lonely runner - but he runs for the grand old party which holds the Senate and the House and may as well get the next presidency and had it in the past more often than not. This makes a really bad impression. I guess politics and entertainment do not go that well together than one usually thinks.
American parties can't exclude people like that until the primary. That's when the party leadership gets together and makes the judgement call on who to send to the electoral collage contest. Everything up until the primary is pre-show and not worth much. Some of party leadership is bound by the popular primary vote, some of them aren't, depending on the state.
It's not really possible to exclude candidates for 'incompatible views', and if party leadership even tried to do that everyone would be upset about it. The most party leadership can do at this point is not fundraise for candidates they don't like. Trump is connected enough with the entertainment industry that money is not a problem, so party leadership really has no hold on him. He just has to be defeated in the primary, i.e. not selected as the party candidate.
Trump is a Republican party member, so he's running in the Republican primary. He'd need to personally declare himself an independent to avoid that, and he'll never do it.
TL;DR American parties are very different from European parties. Party leadership doesn't and can't exert control like European parties can afaict. The only unusual feature of this election cycle is that the media decided to get into the election cycle way ahead of their usual start time, so the pre-primary group of candidates is being treated like it means anything. No one is running with the official endorsement of either party yet - that only happens after the primary.