Way more info than you probably wanted coming down the pike.
What we think of as one monolithic entity as “soap” is actually a metric potload of various chemicals and substances that allow oils to be physically discouraged from sticking to a substance (skin, hair, clothes, dishes) so that those oils can be washed away with water.
So: you’ve got your various types of soaps.
Castile soap is a good example of vegetable-fat soap: it’s made of vegetable oils (traditionally olive oil from Castile, but not so much anymore). There’s lots of recipes for various vegetable soaps, and generally (tho not always) they are more gentle than the other kinds I’ll list below.
Next you’ve got your animal-fat soaps. You’ll have to make these yourself, or get them from organic farms or farmer’s markets: goat-milk soap is particularly common around here. You might remember the making of soap from rendered lard in pioneer books like Little House on the Prairie.
Next up are our industrial soaps: the bars you get like Ivory or Lever or Irish Spring, made from an industrial process with potash. Interestingly enough, “beauty bars” like Dove don’t actually HAVE any soap in them - that’s why they’re so gentle - they’re solid forms of moisturizer with no actual surfactants.
Next we get liquid soap: basically take regular soaps and put lots of spirits of ammonia in (spirits of ammonia are also what we think of as victorian “smelling salts” oddly enough). Liquid soap is way useful, because it’s liquid, so it gets into the articles being cleaned much better than the common alternative which was solid flakes of soap. This development is what brought about shampoo, liquid hand-soap, liquid body soaps, liquid dish and laundry detergents, and all that. Yay progress!
So, all soap is chemicals, and it’s all nasty when you think about it, but if you really want to be good to your skin/hair/system, you want to think about what you’re trying to achieve.
If you want to be as clean as possible, an antibacterial liquid soap is your best bet (please don’t do this, it isn’t healthy.)
If you want your skin or hair to be less traumatized by the surfactants you’re using to clean yourself, then go for a moisturizing soap, or a nice gentle vegetable soap like castile or a gentle animal-milk soap.
If you want to skip the surfactants altogether, then you can go with something like Dove for your body, or even more old-school and rub yourself down with oils (argan is the darling of the moment, but coconut and almond are both excellent choices) and then scrape away the dead skin and dirt that are loosened by the oil massage.
For your hair, lots of people are going “no-poo” (a truly unfortunate name) which is a modern re-discovery of the basic fact that people in the Dark Ages and in Shakespeare’s time knew: hair doesn’t really get horribly dirty - the SCALP gets horribly greasy. If you massage baby powder into your scalp regularly and rinse it out completely, you don’t really have to use soap to keep your hair clean, and if you go further and skip the powdering and just let it keep getting greasy, at some point it will stop getting MORE greasy and you get to decide if you can live with it at that stasis point. Most ‘no-poo’ people use conditioners labeled for fine or thin hair, or that have the words “light” or “clean” in the descriptions.
Or, just use the castile soap in your hair. Take a medium or large bowl (depends on how much hair you’ve got) and make a lather with the soap in the bowl until you’ve got a nice soapy water in there, and then just wash your hair with that. Helps to have a partner for this part, because it’s just as flowing as regular water, so harder to get it into your hair unless you’ve got really long or really short hair. But it works just fine.
I will say that most hair really appreciates having SOME form of conditioner, especially if you are using non-modern shampoo that doesn’t have all those nice modern additives to keep it shiny and smooth and non-frizzy.
Now you know way more about soap than you ever wanted.