I probably do more cleaning than most people in here. I suppose there might be some health effects associated with frequent contact with cleaning chemicals, but I think it's like so many other things we come into contact with... if our body doesn't know what to do with a chemical, it just lets it slide on by to get pooped out the anus. And, that's true for most substances. If you swallow tomato seeds or mushrooms, (or even a button) which don't get digested in our stomachs, you end up finding them in the toilet bowl.
So, unless a chemical is known to do harm, my feeling is that most of them don't do anything to us, but help fill the toilet bowl.
Where you wanna be a lot more careful is when you're handling chemicals that were meant to do harm, such as spraying insecticides and herbicides. Those are chemicals that were made to interfere with the metabolism of plants and bugs (sometimes animals). In that case, then you definitely don't want to inhale the product's vapours or have it in contact with your skin.
The difference between a "soap" and a "detergent" is that soaps are semi-natural products formed by the combination of a plant oil or animal fat with a strong alkali. Soaps aren't produced by any natural process, but they are made by a chemical reaction between two completely natural chemicals, which makes them semi-natural in my books. Detergents tend to be chemically similar to soaps in that they have a long hydrocarbon chain with an active group at one end of that chain. Soaps have been used since Roman times with no noticable health effects, and the strong chemical similarity between soaps and detergents would suggest that detergents are probably pretty benign too.
You can learn a lot about soaps, detergents and the science behind cleaning at the Soap & Detergent Manufacturer's Association website at:
The Soap And Detergent Association
For example: Did you know that the reason you never get any soap scum in your kitchen sink is because you don't use bar soap in your kitchen sink. You use dish washing detergent in your kitchen sink. You use soap in your bathtub and bathroom sink, and soap scum will form in both the bathroom's tub and sink as a result of dissolved soap losing it's solubility in water because of a reaction with the hardness ions in the water. Modern detergents, like dish washing detergents, can be formulated so that their solubility in water isn't compromised by hardness ions in the water, and so they never lose their solubility in water. The result is that even though you can get soap scum rings in both your bathtub and bathroom sinks, your kitchen sink will remain soap scum free.
And, this is just my own hypothesis, but the mildew that grows on bathroom walls (and especially bathroom grout lines) is like every other living thing in that it has to eat something to survive. It strikes me that soap is made from animal fats and/or plant oils, and both of those are high calorie foods. It would seem to make sense that the source of food for bathroom mildew is the natural plant oils in the bar soap used in the bathroom. And, that would suggest that by using a synthetic detergent in the bathroom instead of bar soaps, people could possibly eliminate the mildew from their bathrooms by starving the mildew to death. I'd certainly be interested in knowing the results if someone wanted to try using only artificial detergents exclusively in their bathroom instead of bar soap to see if it eliminated the mildew.
Also, our word "soap" almost certainly comes from the name of Mount Sopa near Rome. In Roman times, Mount Sopa was the place where common people would make a plea to one of their Gods. The process involved pleading for the God's personal intervention in your affairs whilst you burned the body of a small animal as a tribute and offering to that God.
Roman women noticed that washing their clothes in the streams that flowed off of Mount Sopa after a rain would get them cleaner than washing in those same streams at other times or in other streams. Obviously, the Romans didn't understand why that might be, but we currently suspect that the fat dripping off the sacrificial animals would mix with the alkaline ashes of the fires to form a crude form of soap. The rains would then carry that soap into the streams where it would help in cleaning the clothes.
Roman historians record that Romans made soap for use in the Roman bath houses, but how it was used isn't known. It may have been used for cleaning the same way we use soap today, or it may have been used like a skin balm or ointment, or it may have been used purely to make the water bubbly. There is no direct evidence that soap was intentionally made for cleaning purposes during Roman times.