Wow. it's not just those groups either.
How can they make such a fundamental mistake like that?
As for avoiding those products, a lot depends on if you are a dietary vegan or vegetarian, or actually a lifestyle vegan/vegetarian. if you are the latter, then you will already know about most of the alternatives which are readily available. Shampoo and conditioner are something I have raised in the past here on CookingBites. a surprising amount of shampoo and conditioner is suitable for at least vegetarians. vegans have a slightly harder time but soap such as the Greek's make, their famous olive oil soap, is vegan and dirt cheap. both lush and the body shop have plenty of ranges that are vegan and all I believe are vegetarian. most won't say the little things like vegan or vegetarian, but will simply say free from animal products. it scared away fewer customers!
Toothpaste had for many decades been an issue. kingfisher is the week known alternative in the v world with many health food shops stocking it. the same applies to washing powder and conditioner, cleaning agents for the home, anything that contains a surfactant. I studied them for my PhD making my own from scratch. it's not easy and it's why the industry continues to use the waste products left over from the meat and leather industry to make surfactants. and it's not just tallow (fat) that is used. any waste product is boiled to extract what lipid (hard or soft or liquid fat in any form) from bones, skin, waste organs, skulls, brain tissue etc.
What I find more surprising is that people accept this use our just turn a blind eye to it. I don't understand how people accept smearing animal products, often waste products at that, over their teeth to clean them, or over their skin or homes, children etc. I don't get it.
to accept it in things like paper, plastics such as bank notes etc just seems like more exploitation of animals farmed, born, raised and slaughtered in unnatural conditions, unnatural life spans and often inhumanely at that. it just seems wrong and for me.,it is that side of the industry I have issues with. I actually have no issues with animals raised in conditions similar or better than they would be in the wild, allowed to live their life out to the full and bred naturally. allowed to die naturally and then their bodies used to some extent. incorporating them into back notes is one step too far for me.
It's the same 'argument' I have with wool. I use second hand wool, often reclaimed by me from garments people are throwing away, rewinding the wool, dealing with breaks and then making them into 'new' blankets that people cherish or see regular use in my own home. I'm knitting one such blanket at present. there is very little new yarn in it and I won't by artificial wool because ironically it too had animal products in it! not wool, that will last decades, but again, fat extracted waste products and made into plastics which is what most artificial yarn is. t
As for how we keep track of these things, it's actually very easy. some manufacturers you just able completely. but there are lists online kept by the vegan society, the vegetarian society, PETA, and then there are apps which have been written and connect back to these databases. before the internet, it was paper, magazines from the above and word of mouth via health food shops and friends.