Can border patrol really inspect your belongings when crossing from Canada or Mexico?

They can. But in my opinion it is a violation of your 4th amendment rights. But unfortunately the courts disagree with me.

Yes they can and often do....

I am an American by birth and I used to live/work in Canada and travel to the US often.

Been there / done that.

Yes they can, you're entering the United States from a foreign country and there are restrictions on certain things that you're allowed to bring into the country.
Border guards have the authority to search you, your vehicle and your luggage.

ya i hate it too🤷‍♂️