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

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.

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.

Are LGBT people accepted in Japan?

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

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.

“None of my business” is the common attitude.

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

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

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

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How do you see these below?

Yaoi

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

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

Moreover, buff guys are often avoided for their narcissism.

Visual-kei

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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.