What does "mostly" modify?

Solution 1:

Mostly is an adverb modifying the verb are, and means ‘on the whole’. Its grammatical function is no different from a number of other adverbs you might put in its place, such as predominantly, mainly, largely, principally or primarily.

Solution 2:

The adverb mostly has at least two meanings.

1) for the greatest part, in large part, almost entirely
Your post is mostly a copy/paste.
My new shirt is made mostly of cotton, with only a small percentage of polyester. These are mostly silver, but we have them in gold too.
2) on many or most occasions, usually.
She studies mostly at night, but sometimes during the day too. She mostly studies at night, but on an odd occasion she does goes out.
3) chiefly [I am not 100% certain this meaning exists, but I see it in some dictionaries.]
This is mostly a question of ethics.

Your statement allows for all three meanings:

1) most of your friends are non-smokers (via: it is almost eniterely true that all your friends are such that they are non-smokers (some adverbs can be moved to the beginning of a sentence));
2) all of your friends are, on most occasions, non-smokers, but on a chance occasion they are so disposed as to be smokers;
3) your friends are, which is more important than anything else of importance in this matter, non-smokers ("— that they are Big Tobacco apologists and marijuana consumers, is of lesser importance in this discussion about how to raise kids not to become smokers!").

Let us put aside the meaning 3). Most probably, you were implying the meaning 1). Still, only somewhat less probable is that you were intending to express both 1) AND 2), even if subconsciously.

As a reminder, adverbs can modify verbs, adverbs, and adjectives; adverbs cannot modify nouns. In different terms, on the level of sentence syntax, adverbials can modify predicates, adverbials and attributes; adverbials cannot modify one-word subjects and one-word objects.

The adverbial mostly modifies the entire nominal predicate are non-smokers (which consists of the copulative verb "to be" in the third person plural present form and of the predicative nominal non-smokers, which in turn is just a prefixed noun). Your mostly does not modify the verb are with disregard of that verb's having a copulative function in the sentence's syntactic structure. Not that a thing of that sort would be impossible: one can say, accompanied by either articulated or written emphasis, My friends mostly ARE non-smokers, whereas your friends mostly WERE non-smokers., where mostly has little to do with the rest of the predicate, such like in the following sentence which doesn't even feature a compound predicate, and thus in which are is not copulative: We think; therefore we are, just as Descartes' coevals thought and therefore were.

A subject with a nominal predicate is akin to an adjective-modified noun (in which the adjectival function is performed by an attributive noun): a phrase John is asshole is akin to the phrase asshole John. Both phrases can equally plausibly be imagined as a one-sentence retort in same contentious situation. In terms of word classes: [noun][copulative verb][noun] is akin to [adjective][noun]. Syntactically expressed: [SUBJECT][NOMINAL PREDICATE] is akin to [ATTRIBUTE][SUBJECT]. Likewise, friends are non-smokers is akin to non-smoker friends, and my friends are non-smokers is akin to my non-smoker friends (ordering of determiners and adjectives is subject to rules). How to insert mostly into this? Simply. Adverbials can modify attributes, and my is an attribute. Can a pronoun my be the attribute in a sentence? Sure; when pronouns are used to modify a noun rather than stand in for it, they function as adjectives/determiners; it's known to all that adjectives are attributes, on the syntactic level, and likewise are determiners attributes. Now that it's established that my is an attribute, and because we are reminded that adverbials can modify attributes, we know that we are allowed to insert mostly, and we deduce that:

The phrase my friends are mostly non-smokers is akin to a phrase mostly my non-smoker friends.

But, wait, it's already been established that an adverbial cannot modify an attribute! In the latter phrase, the adverbial mostly stands right before the attribute my non-smoker, as though trying to modify it. ¡No pasarán! OK, but an adverbial can modify a predicate—and that's what it, actually, does, albeit implicitly; so, let us discover what predicate that is in this incomplete sentence implied, our adverbial modifies. And let's include it, thus completing the sentence (save for punctuation).

• mostly my non-smoker friends exist
  Or, by reintroducing the less existential synonym:
  mostly my non-smoker friends are

That sentence consists of the words identical to those of the original one (though the reordering of words has changed the sentence's meaning).

This compels the realization that, in order to use the adverb mostly in a way that without the average listener's puzzlement DOES NOT MODIFY the sole predicative nominal, but, more clearly, modifies the entire nominal predicate (it can also modify the entire clause, but in the provided example it so happens that it is nonsensical to attempt to qualify that clause by mostly, so obviously the adverb modifies something other than the entire clause), one might choose to place mostly at the beginning of a sentence. (A comma is therein necessary.) Like this:

• Mostly, my friends are non-smokers.

There is no ambiguity any more as to what part of sentence mostly modifies. There is a comma, so no one in their right mind would think it modifies the subject. This is meaningless: "very, woman."

"No ambiguity" is there—syntactically. That's helpful for school testing. :) Semantically, or perhaps pragmatically, there might remain that ambiguity, which meaning of mostly was intended: 1), 2), or 1) & 2). Your example is not most exemplary of the problem at hand, as "being a non-smoker" is an action/state that cannot be incomplete, except in the sense of continuity. Taking "always" for the time of of action/state, you cannot 'partially "be a non-smoker" '; however, when the meaning permits discontinuity, as the chronological version of mostly does, you can still "be a non-smoker" even if you take a puff once in a blue moon. I give here a different example, more illustrative: Soft drinks are mostly sugar. For the action/state of "being sugar", both frequency and integrity indeed are modifiable.

One other point. Adverbs normally go after the subject and before the verb. For example, Dogs often bark. However, when the predicate contains a copula, the adverb normally goes after the copula: War is always hell. "Normally" mainly refers to the lack of emphasis, which implies articulation (cf: War is ALWAYS hell.) and/or pragatically neutral stressing of the sentence elements (War is hell always. Always is war hell.)

So, in the sentence My friends are non-smokers., the adverb mostly is positioned in a normal fashion. Even though it's positioned after the verb, it doesn't modify something other than the predicate. When an adverb is put at the beginning of a sentence, it receives additional stress, additional importance. The so generated nuance may be unsuitable for someone's intended meaning.

Finally, I've found on the internet a similar question: Cotton fiber is mostly composed of celluose. or Cotton fiber is composed mostly of cellulose?

In the first sentence, analogous to your example, the adverbial mostly modifies the adjectival predicate is composed of cellulose. In the second sentence, the adverbial mostly modifies the attribute composed of cellulose (we've established that adverbials can modify attributes), which acts as a predicative adjective part of the entire adjectival predicate is composed of cellulose, which predicative adjective in turn consists of two components of which both are acting as adjectives and are set in the "adjective-modified adjective" form (such as hot red, which is evidently [adjective[adjective]]), in which form the first adjectivally-functioning component is actually an adjectival passive (past participle) composed, and the second adjectivally-functioning component is the adjectival phrase of cellulose, which is composed of the preposition of and the noun cellulose. OK, that sentence was a mouthful and a headfull.

Please correct my mistakes if and when you discover them.