Comte was an altruistic occultist who learned the principals behind his definition in various initiate religions and groups teaching "mystery" religions thousands of years old.
His idea is that all parts of existence are in some way shape or form connected to and affected by all other pieces of existence. This is believed to be on more of an energy or spiritual level than anything else.
This isn't to be confused with modern day new age tree huggers. They may have read some books from the local "enlightened store" on eastern philosophy but largely have jumbled multiple ideas up in to poorly understood hippie garbage.
Anyways, the idea that all men support all men is believed on a deeper level than socialism, charity or what have you.
It is the idea that the life force, soul or what ever you want to call it, in every being, is contingent in some way to every other being.
Like a cell kind of. In one cell, "the world", you have mitochondria, lysosomes, ribosomes, golgi etc, and a nucleus that makes it all work.
Supposedly we are all the various parts of the cell. We are born with a specific function to the cell, much like each part of an actual cell carrying out a specific purpose.
The nucleus is God, every culture has it's own definition for God but recognizes the existence of a powerful deity orchestrating and administering the law that binds all of the cell's functions together to make a living, working organism.
Altruism means you are in some way, recognizeable or not, responsible for everyone else in your cell and vice versa.
People extrapolate this belief and form social and political philosophies off of it but that form of charity isn't true altruism and you can't really compare Ayn Rand's economic ideology to literal altruism.
Then you have analogies comparative to physics, stealing electrons, uniting various atoms to create new matter etc. "Ritual Magick" is another topic Comte studied.
Ritual Magick is also largely misrepresented, instead of being butchered and misinterpreted by hippie, feel good, save the whale types, Ritual Magick is given a bad name by reject teenagers with fake vampire teeth and a mind full of "HATE!!!!"
Think more along the lines of Comte, Alastair Crowley, Neville Chamberline, Winston Churchill, Nostradomus etc.
You can't compare or contrast mystical belief and practice to social, economic and political philosophy.