The biggest concerns I've seen are general anxiety with their national security setting seeing as they're right up next to China. They're very dependent on the US for security and so since probably early 00's there's always been mild talks of them strengthening the SDF and improving their military standing (reversing Article 9). Japanese folk are still sensitive to the topic of war so any movement towards making that change serious have been very gradual.
Japan is already very conservative, but not religious. Their politics had been depressed in previous decades. There was some controversy around the time of Bush Jr with a prior PM (Junichiro Koizumi) visiting and signing the logbooks at
Yasukuni Shrine for the war dead (soldiers). This was seen as really controversial.
The US (and UK) are really more unique than we give it credit for in that we consistently remain energized and actively engaged as a populace in our political systems. That's almost entirely because of the way our culture both functions and operates down to the individual level and how Westerners see themselves as voting bloks. Japan was forced to move away from fanaticism after a very devastating war. Neither of our countries have been on the losing end of a major war or watched portions of the population die off from starvation, so the social pressures there also aren't comparable. The idea of going backwards isn't seen as an ideal in this instance.
Japan's economy has been in a low grade economic depression since about the early 90s and so anything relating to "great again" might be a stretch as a huge block of the voting population will not have recalled "when it was great" (pre-90s). I know places like Kyoto have changed dramatically thanks to tourism and residents do want to claw back control of their culture centers before they're lost completely to consumerism.
As for "far right" talking points, there's the crime that migration has been brought and in Japan even occasional incidences stand out. However, those pressures have always existed. Ex: Around the American bases at Okinawa there were spikes in things like rapes, etc and a portion of that population was becoming strongly opposed to military bases locally on the whole. That was a movement during the late 90s, iirc.
Comparing these motions to "make great again" is an easy argument to make. Obviously in election cycles where things are doing poorly (like the economy and birthrates), the most lucrative options for "be better" will stand out on the ballot sheet. So to say that it's on the same level as why America went MAGA is a stretch, I think, but Western media will have a field day trying to paint it as such because that's going to generate more clicks.
Japan obviously requires some immigration and most everything they need has to be imported in since it is an island economy. I know folk that moved here who work for the energy sector there that have to take energy they produce here and export it. Only recently did they restart some of their nuclear reactors post-Fukushima.
I don't know that the average Japanese person thinks about feminism as we do. Modern Western feminism and identity politics doesn't work at all with their work culture (or ethic for that matter) Still Japan has been more open to changes in recent years, for example, same sex marriage has a 70%~ approval rating:
Politics contradict Japanese public opinion on same-sex marriage
https://eastasiaforum.org/2024/06/15...-sex-marriage/
I have seen identity politics/"Feminism" try to make its way there through media. Ex: Japanese articles that were very clearly written by someone who was indoctrinated ahead of time with almost 1:1 talking points out of Western critical race theory. The kinds of talking points that don't really make sense for the average Japanese person. I would think least some nations across the world have become sensitive to these ideologies seeing as they not so casually sprung up out of no where. So the negative aspects of it that have occurred in the West, it's understandable more isolated/homogenous cultures (like Japan...) would be cautious.
Japan would be sensitive or insensitive to Westernization. It depends on how you look at it. Western influences comes through media, but also the American<->Japan social frameworks from post-occupation. There's also the fact they're highly dependent on maintaining strong exporter/importer relationships.
However, to say Japan isn't thinking for Japan and is copying our model especially socially (which is most of your points), I think that isn't correct. It's only maybe in the most recent decade when relaxed attitudes towards immigration appeared. I remember because when I was looking into work requirements there, the foreign population was still quite low and permanent residency was still very difficult to acquire. For one, they required you could self-support and that applicants could pass the language proficiency test. (JLPT)
So I don't know that this was a "far right" backlash as Western media is making it as there is a lot more involved. America has been shifting its own foreign policies for a while to be more isolationist and understandably Japan is beginning to think more heavily about its own concerns. I'm totally aware Trump has a weird fan following in many nations (not just Japan) and that can be seen via "Japan First" rallies.
I think most countries are completely on board with migration in general as long as their economies could support it. Japan ebbed along without any real changes to their economy and they needed to have thought about making changes a while ago because their tax base is shrinking considerably as their population dies off and it will be increasingly difficult to keep their economy going without mass migration. They have universal healthcare and a pension system I believe, much like the UK, and undoubtably those are strained by an aging population (30% are 65+... 36.25 million in 2024 on a quick lookup).
As for religion, I don't know where that point comes from... Japan has its own religion (Shinto) but many don't directly follow it in practice as that would be impractical. One of the things the Japanese had to renounce during surrender was the imperial state. That meant that their Emperor had to declare he was mortal (ie not actual God). Christianity does have some presence there but it's not in an evangelical-form like our Christianity tends to take in the West. They don't even celebrate Christmas the same way we do. It's more of a romantic holiday there and most holidays focus around family dinners and other secular activities.
I can't say I'm an expert on this topic, but I know enough to know it's not similar. There's probably other differences I'm not aware of, but political enthusiasm is almost certainly more Western than that... In all fairness I asked my friend about the result and he said "It was amazing", but in Japanese and with a muscle man emoji. So maybe that makes all my points completely useless lol /s. We don't talk much about politics because it's not very Japanese, but he has lamented for a long time the loss of families. Having children were a major motivator for him in life. He left a really well-paying life long job in the city to move back to rural and pursued certification with the government and also took a teaching post. He said he couldn't be there fully for his children prior and was missing the memories. His wife was struggling in that role full time, also. Japan's work requirements (compared to Western standards) are often insane so a low birthrate isn't really all that shocking...