Whatever Ben Shapiro is, alt-right or just right of center, he holds views typical of most conservatives. If that means all the U.S. conservatives meet your definition of alt-right, so be it.
This. None of these are static categories, and even if Shapiro's litany of X-phobic views were previously 'alt-right', they are now part of the mainstream political right (and its manifestation in the Republican party). As a result I think it's genuinely hard to be a non X-phobic conservative these days.
This kinda parallels the alt-rock of the 90s as mentioned in other comments. Back then it was called that because it was "alternative" to what was mainstream rock, but over time it eclipsed the mainstream and now most new rock music falls under the "alt-rock" umbrella.
To continue with alt-music analogies, I am a big fan of alt-country (bands like Wilco, Son Volt, etc) who were the alternative to the dominant pop-country genre. IIRC in recent years that genre has influenced pop country but never really merged with it.
