Paging through the Google results I see 131 for "the Klingon are" and 170 for "the Klingons are". If you eliminate Google's weird inclusion of the greengrocer's apostrophes, it would look like "Klingons are" is only about a 2:1 favorite on the web. I suppose people think of it like "the French." Google NGrams do tell a different story: http://bit.ly/2INR9wI.
I'd never noticed the plural "Klingon" before, but you're right, it's everywhere. I wonder how much weight this quotation, published in the Washington Post, is placing on that scale:
"The Klingon are a very, very direct culture -- not subtle at all," says Marc Okrand, a student of their civilization who converted their society's attributes into words, phrases and idioms when he developed the Klingon language."
I don't remember hearing Marc use "Klingon" that way. We'll have to ask him.