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

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.

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

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).

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

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.

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.

What do bad boys know that nice guys don't?

Visual-kei

Moreover, buff guys are often avoided for their narcissism.

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

What great song was "ruined" once you really listened to the lyrics?

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

Yaoi

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

What are some tips for making your husband fall madly in love with you again after going through the worst phase of your marriage?

“None of my business” is the common attitude.

How do you see these below?

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

Do you think a lot of sociopaths' parents kill themselves for having brought such disgusting evil into the world? How much shame and disgust must they carry?

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