Why should the law care about what I do behind closed doors?

But what if you're raping little girls behind closed doors? Killing gay men? Watching child porn?

Liberty is not boundless. It does have its limits.

You can stand on a public sidewalk and take pictures of my house. You can't walk into my house uninvited and start taking pictures.

Can you fly an American flag in the UK in your own private property there? What is the UK’s government stance on that? And if yes, do you also have to fly the UK flag or the American flag can fly solo?

If evidence arises that you are doing these things behind closed doors, don't you think the government has a moral obligation to investigate?

It shouldn't to a point.

The law doesn't care about what you do behind closed doors as long as it is within the bounds of what the law allows.

This Demonized Carb Is Actually Great for Longevity, According to a Doctor and RD - Yahoo

Society sets laws announcing those actions that it deems unacceptable in polite society. If evidence appears that causes a reasonable person to suspect that illegal activity is going on, society should investigate. Of course society might find itself having to jump through hoops by adhering to constitutional law. It cannot just invade your personal space and demand to know what you're up to just because they don't like you.

Your speech is free. But if it causes malicious harm to someone, you can be sued.

The law shouldn't care (if you are a law abiding citizen) about who you take into the bedroom as long as they are consenting adults. How many guns you own. What you eat for supper. What kind of TV shows you watch. Whether you watch porn or not.

How do atheists explain the fact that when I pray to God, I feel better and I get a feeling of comfort? Doesn’t this prove that a God exists?