Solution 1:

It's not really a question of opinion. Stupider is, as the dictionaries and usage you quote show, entirely grammatical. It is also in rather common use, though less common than more stupid.

The main issue here is that words of more than one syllable tend to resist the -er suffix. Wiktionary's entry on the -er suffix says this (emphasis mine):

The suffixes -er and -est may be used to form the comparative and superlative of most adjectives and adverbs that have one syllable and some that have two syllables.

I believe that people's aversion to this word stems from the belief that "-er is usually used for monosyllabic words" is a rule, rather than a guideline (or, more correctly, an observation). This tendency probably has phonological roots related to stressed/unstressed final syllables interacting with the suffix, but I really don't know enough to say.

If a word has a meaning everyone can agree on, appears in dictionaries and is in use for centuries, this means it is a word!. It might be a word with social connotations of "improper speech" or "bad grammar", but a word nonetheless.

Solution 2:

"Stupider," like "ain't," is often thought to be not a word. It has all the things you would expect of a word. It has a meaning we can all agree on. It appears in dictionaries (so you can find out what it means if you don't know). But it isn't given the recognition of a word, even by many people who use it.

This is a cultural phenomenon, and it's best in most contexts to avoid using these non-words. The problem is that with most of the English-speaking world raised to believe that "stupider" is not a word, you will appear to them to be more stupid if you use it. In short, the word "stupider" carries a stigma. Nothing is inherently wrong with it.

The irony is that some of these non-words have been in use for centuries, while "to google" is already an accepted verb, even with its short history.

edit: apparently my irony was unclear in the first sentence, so I added "often thought to be"

Solution 3:

It's a valid word and, as you say, not even that unusual.

It seems, on this issue at least, you are cleverer than them. They are stupider.

Solution 4:

While OED doesn't list stupider it does contain a citation for the superlative:

1842 S. Lover Handy Andy xliii, She felt the pique which every pretty woman experiences who fancies her favours disregarded, and thought Andy the stupidest lout she ever came across.

So it might be assumed that stupider was in use in the early nineteenth century as stupidest was.

An Ngram confirms this, but it also shows that stupider is the least popular comparator. Perhaps suprisingly, even though -est is usually confined to monosyllabic roots, stupidest has outranked most stupid in British English since around 1870.

(The difference between American English and British English is a little surprising.)