Is the use of a hyphen between "non" and an adjective strictly necessary?
Solution 1:
Yes, a two-word modifier (like this one) requires a hyphen, except that the commonly held convention is that adverbs ending in "ly" don't (like that one). See this table in the Chicago Manual of Style.
Solution 2:
As an addendum to Monica's fine answer, I'd like to add that there is a third possibility: fusing "non" with the word it precedes. A typical example would be "nonrelativistic", which seems to be Merriam-Webster's choice.
Similarly, one reads nonnegative, nonmagnetic, nonferrous, etc.