Good points. I had a big problem with Sarah Beeny and her tame experts as you say they didn't explain themselves properly and contented themselves for going for maximum scare without saying what the relative risks of all these things are.
Its a bit like saying "FIRE IS DANGEROUS" (ok I'll agree) "BAN IT NOW BEFORE IT KILLS US ALL" (Fine, now how am I going to cook me tea now I can't light the gas cooker)
Dramatising a bit, but it leads me to the next point about stuff like SLS and SLES. It comes down to how much you use, and how you use it.
Ms Beeny pointed out that its used to clean car engine blocks. OK might be, but thats as a concentrated industrial cleaner. Shampoo is much, much weaker, so the risks are much much less. Its like comparing vinegar to pure glacial acetic acid (the active part of vinegar concentrated as high as it will go)
A bottle of vinegar is rather nice on your chips, a bottle of glacial acetic acid when uncorked will make you choke, cough and will clear a room in seconds.
Back to SLES, thats used in the shampoo because its cheap, foams and washes well, and is harmless to your skin in those levels. There are other "More natural" detergents, but they are 3 times the price, a bit milder maybe, but they don't foam and wash as well.
The Methylparaben is in there to keep the stuff from going off. Its a reasonable bacteriocide, and is pretty good against moulds as well. Of all the preservatives that are legal, its also the one least likely to give you an allergic reaction.
As for more different parabens being worse, thats strangely enough the opposite to whats true. Theres a thing called the Parabens paradox which means that a mixture of parabens such as Methylparaben and Propylparaben is actually causes less irritation that just one on its own. Thats reflected in the regulations as well. legal limit for 1 paraben 0.4%, legal limit for a mixture, 0.8%.
Methylchloroisothiazolinone, I'm not a fan of as it can cause problems for people with very sensitive skin. If you're not in that part of the population, its not a big problem.
Parfum can be an issue for some people, but there are a lot of unfragranced products out there if you don't want to go that route. Every big brand appears to have at least one in the range, and other brands make a big thing about it and everything is fragrance free across the board. Also a lot of fragrances contain essential oils, even the cheapo ones. These contain allergens too, and can cause a problem if they're in at strong levels.
Antibacterial handwash isn't something I'm a fan of, plain old soap and water is perfectly good at cleaning crud off. If you're having to wash your hands a lot you may prefer handwash, as you might find it less drying to the skin.
A good site to look at is the sense about science one
Sense about scienceIt may give you a better idea of what makes for good science and how to spot the more dubious claims.
In all things, find out, educate yourself, and don't always believe the hype