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

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.

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.

It shouldn't to a point.

The doctor said 'be happy.' Music therapy can help cancer patients do that - NPR

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

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

Liberty is not boundless. It does have its limits.

Could humans be selectively bred, like dogs, to create 2 subspecies that can no longer have offspring? Do I not understand selective breeding properly? Im not worried about the moral implications, just the science please.

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.

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

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.

“Intelligence Evolved Twice on Earth”: This Groundbreaking Discovery Redefines Life Itself and Shakes the Foundations of Evolutionary Science - Rude Baguette