Your linked evidence doesn't support what you say. There are plenty of examples of concerning ingredients turning up in tattoo inks (a recent study found many inks have unlisted and potentially harmful chemicals[1]). This is obviously not good, but it falls far short of "causing" anything in particular. It's similar to all the warnings in CA about "chemicals known to cause cancer" - unless you would also say something like "putting gas in your car is known to cause cancer." Tattoos are not known to cause cancer and the articles you link don't claim they are.
It certainly can - I think artificial sweeteners are great examples. There are experimental studies that show that artificial sweeteners can cause cancer in animal studies, but as of yet there's no clear evidence of that showing up for any definable population in the real world[1].
Chemicals linked to cancer (or other conditions) are cause for concern! It's important to note & track these things. But the dose makes the poison and it's totally possible to inject a chemical that 100% causes cancer (under some circumstances) with no adverse impacts.
You are talking about non cancer causing chemicals to humans. The definition of a cancer causing chemicals is it will cause cancer. If it's a small dose it will not be easily detectable that doesn't mean it doesn't cause harm.
Everything is about dosage. Even a small enough amount of uranium isn't harmfull and is quite normal. It's at the point where trying to avoid it will cause more of an issue.
Trying to avoid tattoos doesn't cause any issues. Radiation is normal in nature. Injecting lead into your epidermis isn't. Any amount will do harm just like 1 cigarette is worse than 0.
Radiation is normal in nature and will give you cancer. That's the main reason why people wear sunscreen[1]. It's not like there's a "natural" amount of radiation that is 100% safe and then you cross a boundary.
I agree that avoiding tattoos is harmless. Tattoos have no "benefits" - but those aren't the statements we are critiquing.
> just like 1 cigarette is worse than 0
This is almost certainly not true. Nicotine has a number of properties that might benefit you in the moment, or under certain conditions[2]. Cigarettes are not "healthy" and they are never going to be the "best" delivery system, but there exist many situations where your health would improve if you have your very first cigarette.
Another good example is that Vitamin D, which is an essential nutrient, can cause increased cancer risk[3]. Looking at substances as "causing cancer" or "safe" will lead you to an inaccurate understanding of when you are taking risks and when you are not. You can't live without Vitamin D and also if you get too much it can help give you cancer.
[1] https://news.ycombinator.com/item?id=39542567