Your first translation is the (almost) correct one:

Je sais que c’est frustrant mais il vaut mieux se taire. Tu sais
comment ils sont pour tout ce qui touche à l’ordre [public].

It means for “for whatever is related to the [public] order”. Your second translation means “for all these [people] who have business with the [public] order”, which is a very different meaning. From your question, I understand your intent to be the first one.

Warning

This answer is the result of a misunderstanding of the actual question, so it is a bit beside the point, as indicated by the first comment below it. I removed it, but then realized someone cited it in the comments below the question, and someone proposing another answer also mentioned he thought it contained useful information (for some reason…). So here it is again.

Toucher doesn’t mean déranger (follow the links to look for one word within the definition of the other one: one unrelated hit for Destouches in déranger, no sign of déranger in toucher).

They can be close to each other under certain circumstances, but they still represent two distinct concepts:

• One can prevent or discourage people to touch things, lest they disturb some type of order, damage or break something, and indeed in some cases the slightest touch may have a consequence, but touching and breaking remain two different things, the former simply sometimes triggers the latter.

  • Museums and other institutions that display precious or fragile items commonly display a warning requesting “Touchez avec les yeux seulement”:

  

However, in a strong injunction of the form “Touche pas à (usually a possessive) (something)” (eg. “Touche pas à mon drapeau”), the verb toucher is indeed used to warn people of consequences, should they touch whatever is specified in the address.

If a possessive is added, and probably an adjective to explicit the perceived importance of the order, the sentence proposed in the question could possibly work, making it appear like they seem to believe they own the (public) order (it could actually also work with minimal adjustments for l’Ordre des médecins or some other professional, religious or other official Order):

• Je sais que c’est frustrant mais il vaut mieux se taire. Tu sais comment ils sont pour tous ceux qui touchent à leur sacro-saint ordre (public).

“ce” = ceci, cela = something (whatever)
“ceux” = eux = some people (whoever)
The remaining part of the sentence has the same meaning.
(Sorry for the poor sentences above).

Uniquement en ce qui a trait à la deuxième question. On trouve pour toucher le sens « apporter des modifications, des corrections; en particulier, modifier en portant atteinte, en dégradant quelque chose. Toucher à un texte, à un vers; toucher à une loi, aux libertés, au droit de grève. » (TLFi) sauf que déranger n’est pas modifier et dans ce sens-là plutôt que dans celui de s’intéresser/concerner, ça constituerait à mon avis une extension de sens abusive. Par ailleurs je ne dirais pas non plus qu’on dérange l’ordre public quoiqu’on puisse déranger l’ordre de quelque chose. On peut probablement porter atteinte à, aller à l’encontre de, s’opposer à, une chose peut être contraire à l’ordre public mais des personnes peuvent surtout troubler l’ordre public, la paix, dans le sens de perturber.