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.

How do you see these below?

My boyfriend won’t tell me his past and it hurts me so I broke up with him what do I do?

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

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

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

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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.

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 so-called “couple culture” seen in many Western countries.

I see ugly guys dating gorgeous, "hot" women all the time. I, too, am not very attractive but I'm not doing well with the ladies. What's their secret?

Yaoi

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

Moreover, buff guys are often avoided for their narcissism.

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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.

Visual-kei

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

Are there any more 'nun' jokes?

“None of my business” is the common attitude.