I do not think the historical analogy is so clear-cut.
However, there is a mindset on the part of some who champion going up to Hat Habayit that scorns anyone who won’t go up to Har Bayit (and won’t join them in poking their opponents in the eye) as some kind of Galut-mentality weaklings who kowtow to the goyim. Rabbonim who oppose going up to Har Bayit (including some very notable Zionist rabbonim) are simply ignored.
A friend of mine goes up to Har Habayit on occasion. But he told me that he goes to daven, not to make a point, and that he sees his visits to Har Habayit as very personal & very private and nobody else’s business. I contrast this with the parade of politicians to Har Habayit who go not to commune with Borei Olam but to make a point, to get their names in the headlines and bolster their political standing among whatever constituency they cater to, and burden the police who must allocate resources (that could be used elsewhere, say, in the war against crime) to protect them.
The gratuitous, triumphalist let’s-rub-the-Arabs’-noses-in-it aspect of it reminds me of those Protestant Orangemen in northern Ireland who periodically march through some completely Catholic neighborhood to mark some medieval battle in which the Catholics were routed. Ugh.