I'm looking to describe an effect caused by using a particular construction in English, and the fact that it affects the listener and the whole of their thought processes without the listener being aware of it. The words insidious or pernicious would almost do, but these have negative connotations. The effect here is neither positive or negative.
The use of (x) has a(n) _____ effect on our mental processes.
That sentence requires an adjective, but an adverb would do just as well :
The use of (x) affects our mental processes _____ .
So, a quick recap. Ideally the word would:
A stimulus that is below the threshold of conscious perception, but nevertheless influences one’s mental processes is said to be subliminal, or to influence them subliminally. As the OP requested, characterising some influence on a person as subliminal, does not imply anything as to whether the influence, or the motivation for it, is good, bad, or neutral. The Wikipedia article on the topic provides a serviceable explanation of the concept. The term started out as a technical term of psychology, but quite a few people have by now heard at least some popular outline of this phenomenon to be able to understand the term. In informal speaking and writing, the term is often used more loosely than among professional psychologists.
a. So slight as to be difficult to detect or describe; elusive: a subtle smile.
b. Difficult to understand; abstruse:
The use of (x) has a subtle effect on our mental processes.
to pass into or through every part of
to be diffused through; pervade; saturate
In this particular context, I would use subconscious1. From Oxford Dictionaries:
Of or concerning the part of the mind of which one is not fully aware but which influences one's actions and feelings.
This is a fairly neutral term, and captures the sense of affecting thought processes without the thinker's conscious awareness. It would work adverbially, as well, so you could say either
The use of (x) has a subconscious effect on our mental processes.
The use of (x) subconsciously affects on our mental processes.
If those don't sound strong enough, you could add a modifier (and could potentially drop the phrase "mental processes, since that is implied in the term) for something like
The use of (x) has various/widespread/pervasive subconscious effects.
1 Or unconscious if you want to be consistent with technical psychoanalytic terminology. However, in a lay setting I think subconscious is at least as common.
Pervasive/Pervasively (meaning, permeates through everything, from Latin "passed through") can and usually does have negative connotations, but does not necessarily have to. https://www.merriam-webster.com/dictionary/pervasive lists "A pervasive rhythm" and "A pervasive sense of calm" as being valid.
Ubiquitous (meaning "present everywhere", from Latin for "everywhere") has the connotations more of something which is everyday and utilitarian to the point of being ubiquitous. However, it doesn't work so well in the OP's example sentences.
Could I perhaps venture surreptitious? Perhaps, again too negative. Its synonyms are given as things like covert, sneaky etc.
Discreet, discreetly, perhaps - Unobtrusive, understated; not ostentatious or eye-catching (OED)
How about ubiquitous? It plays a very similar role to insidious and pernicious without having a negative connotation.
It doesn't fulfill "without the listener being aware of it," but then neither do insidious or pernicious.
transformative - where something changes the basis for thought patterns, not described in a negative or positive way but all-encompassing
How about gradual?
The online dictionary for both insiduous and pernicious say something like
proceeding in a gradual, subtle way...
Gradual is neutral and has no positive or negative implications.
The use of (x) has a background effect on our mental processes.
This word has no connotations at all and merely states that something is not in the foreground. In this case the item is in the background of the mental processes and, thus, is not noticed in the cognitive process but is definitely present as an influence.
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Perhaps non-obvious, "not immediately apparent or such as would ordinarily be expected" (OED), would work. After all, something that is insidious is something that is evil, but not obviously so.
Taken from Google's dictionary:
additional but subordinate; secondary.
"the collateral meanings of a word"
Usage in your sentences:
The use of (x) has collateral effect on our mental processes.
The use of (x) affects our mental processes collaterally.
A word that means difficult to detect, but unlike subtle does not mean the effect is minor, would be:
among its definitions
Hidden from view; concealed
Not accompanied by readily detectable signs or symptoms
An appropriate word may be underlying:
Arguably, attempting to assert that something that "affects the listener and the whole of their thought processes without the listener being aware of it" has no negative connotation is itself insidious and pernicious.