"We do not touch women."
I'm guessing "em as" is still grammatically correct even though "nas" is more used? I haven't learned "nas" yet, only das/dos ás/á and ao so far. So I'm mostly wondering why "não tocamos em as" wasn't accepted while "não tocamos as" and "nós não tocamos em as" was o.O Why is it okay to drop the "nós" only if you drop the "em" at the same time? o.O
The contraction nas (em + as) is mandatory. It's not correct to say or write it separately. There are a lot of other contractions/combinations. Some are optional, some are mandatory. Here is a list that may be helpful: http://pt.wiktionary.org/wiki/Ap%C3%AAndice:Combina%C3%A7%C3%B5es_e_contra%C3%A7%C3%B5es_da_l%C3%ADngua_portuguesa
There is no relation between dropping "nós" and "em" at the same time. Since the verb endings in Portuguese differ by person and number, you can always drop the person out of the sentence. It's possible to know who is the person by how you conjugate the verb. "Nós tocamos" and "Tocamos" have the exaclty same meaning. One can know it's "nós" because the verb ends in "-amos".