I don't particularly agree with claims that Japan is more socially conservative by most metrics, because they are made by Westerners who frame conservatism relative entirely to their own worldview, a worldview which is not particularly informed about the reality of Japan given that Western media constantly reports falsehoods for clicks. But that's not really here nor there.

The subject matter is LGBTQ acceptance specifically. The point about Abrahamic religion is that it creates a culture of extremely open and aggressive hostility towards LGBTQ people. Hatred becomes part of people's foundational beliefs because they believe that is what God demands of them, and they cannot be reasoned with to reach a mutual understanding. While you could cherrypick "relevant metrics" like specific legal rights to rate Western countries as "more progressive", the actual populations are less accepting, in other words your social rights are lesser and you are more likely to face severe discrimination and violence. Those legal rights are also in an extremely fragile state because there are conservative movements to strip those rights. In Japan, indifference is far more common than hatred, and political movements are not polarized around things like "wokeness" or "social justice". Takaichi, widely reported in Western media as ushering in a new era of Japanese hard-right conservatism, has a pretty moderate stance that is analogous to Obama circa 2008; she does not support same-sex marriage, but is not actively antagonistic or hateful towards LGBTQ people.

I would sum it up as this: LGBTQ life in Japan is peaceful. Legal rights could stand to be improved, but there is no fight to constantly justify your own existence, and you are allowed to live without facing significant social prejudice. Most people are accepting, and those that aren't mostly just don't care. There are large supportive communities and extensive cultural representation in media, too. I, personally, would never trade this status quo for that of the US or UK in a million years.