How conservative the Japanese people really is? And the government?

They don’t have the so-called “couple culture” seen in many Western countries.

Yaoi

In the old era, gay relationships were very common and were even praised among the privileged social classes, such as Samurai and monks.

Isn't it ironic people always talk about how much women hate Donald Trump, when almost any of them would marry him if they could? What he said in the 2005 Billy Bush video, almost every woman would share the sentiment if it got them his lifestyle.

I’ve heard it’s always the male side that is expected to take a move in some countries. It’s not the case in Japan.

They don’t have the value that “guys must be macho.”

They don’t bring around their mates everywhere, which means they don’t worry about being single, gay, or whatever because no one cares about whom others are having/ not having sex with.

What exactly is the boundary men should follow while looking at girls so they don't call them perverts?

This is a very vague question. But considering the asker’s comment on Mr. Nakajima’s answer, your interest seems to be in sex-related matters (I don’t think it’s the only indicator of conservative/ progressive, though).

We don’t instantly tie it with sex when a father and his very young daughter are taking a bath together.

How do you see these below?

What kind of pleasure do gay men get from being bottom? The idea is very appealing to me but in practice it's quite painful.

Visual-kei

Moreover, buff guys are often avoided for their narcissism.

They don’t tease or beat up cross-dressed people on the road.

How can someone express their love for a guy without using words? What are some actions that can convey love and care?

I sometimes feel people from the West are obsessed with those “gender” and “sex” things too much. Let’s think about something else sometimes. It’s unhealthy.

They were very similar to the bromance of today but accompanied by sexual intercourse.

“None of my business” is the common attitude.

Islam is definitely a very anti-LGBTQ religion, so why don't liberals ever stage pro-LGBTQ demonstrations at mosques or at the consulates/embassies of Muslim countries?

It’s very common for a girl/ woman to ask a boy/ man to be her boyfriend.