a fewer or fewer?

The problem here is not the word fewer, but rather your (mis)use of the indirect article, a.

People will have fewer choices of foods and consume fewer types of nutrients.

Incidentally, the noun choice is both countable and non-countable; so, you could also write:

People will have a smaller choice of foods and consume fewer types of nutrients.

To clarify Peter's statement, "a fewer" is never correct. The reason for this is that the pronoun/adjective "few" means a small (or, in the case of "fewer," a smaller) number [of things, choices, nutrients, people, etc.] but always a number greater than one.  In other words, "fewer" can only be used with plural nouns, hence the article "a" should not be used with it.  In your case, because you would not write "People have a choices" (instead of "People have choices") or "consume a types of nutrients" ("consume types") you should not write "People have a fewer choices" or "a fewer types." 

I hope this makes sense.