The alt-right is mostly an online movement, which makes it hard to measure. The three main alt-right hubs I know of are /r/altright, Stormfront, and 4chan’s politics board.
The only one that displays clear user statistics is /r/altright, which says that there are about 5,000 registered accounts. The real number is probably less – some people change accounts, some people post once and disappear, and some non-white-nationalists probably go there to argue. But sure, let’s say that community has 5,000 members.
Stormfront’s user statistics say it gets about 30,000 visits/day, of which 60% are American. My own blog gets about 8,000 visits/day , and the measurable communities associated with it (the subreddit, people who follow my social media accounts) have between 2000 – 8000 followers. If this kind of thing scales, then it suggests about 10,000 people active in the Stormfront community.
4chan boasts about 1 million visits/day. About half seem to be American. Unclear how many go to the politics board and how many are just there for the anime and video games, but Wikipedia says that /b/ is the largest board with 30% of 4Chan’s traffic, so /pol/ must be less than that. If we assume /pol/ gets 20% of 4chan traffic, and that 50% of the people on /pol/ are serious alt-rightists and not dissenters or trolls, the same scaling factors give us about 25,000 – 50,000 American alt-rightists on 4Chan.
Taking into account the existence of some kind of long tail of alt-right websites, I still think the population of the online US alt-right is somewhere in the mid five-digits, maybe 50,000 or so.
50,000 is more than the 5,000 Klansmen. But it’s still 0.02% of the US population. It’s still about the same order of magnitude as the Nation of Islam, which has about 30,000 – 60,000 members, or the Church of Satan, which has about 20,000. It’s not quite at the level of the Hare Krishnas, who boast 100,000 US members. This is not a “voting bloc” in the sense of somebody it’s important to appeal to. It isn’t a “political force” (especially when it’s mostly, as per the 4chan stereotype, unemployed teenagers in their parents’ basements.)
So the mainstream narrative is that Trump is okay with alienating minorities (= 118 million people), whites who abhor racism and would never vote for a racist (if even 20% of whites, = 40 million people), most of the media, most business, and most foreign countries – in order to win the support of about 50,000 poorly organized and generally dysfunctional people, many of whom are too young to vote anyway.
Caring about who the KKK or the alt-right supports is a lot like caring about who Satanists support. It’s not something you would do if you wanted to understand real political forces. It’s only something you would do if you want to connect an opposing candidate to the most outrageous caricature of evil you can find on short notice.