This is indeed an idiom. More precisely, it's a corruption of one. It comes from the phrase "drop of a hat":
Bob is always angry. He's willing to start a fight at the drop of a hat.
There's a question at ELU relating to the origin of this phrase. The general opinion is that it comes from the (supposed) Old West practice of an arbitrator dropping a hat to the ground to signal the beginning of a fight.
*How does this relate to the phrase in question? Consider message boards or chat channels. In these communication media, when someone posts something radically opinionated, it tends to start a strongly heated discussion, or even a fight. Someone "dropping an opinion" on the channel, therefore, is someone attempting to instigate.
In the given context, of course, the phrase seems to be used positively, in the same sense as:
Bob is a great guy. He's always willing to help out at the drop of a hat.
"Drop of an opinion" is not standard English, so be aware that use of the phrase could lead to confusion. "Drop of a hat" would be clearly understood by most native English speakers.
**This paragraph is original research*.
It's worth copying in a line quoted by the top answer when this was asked about on ELU...
"Unfortunately, the rules for adjective order are very complicated, and different grammars disagree about the details".
I'd also have to say that "opinion" is a very slippery (not to say subjective) word category. If beautiful is an "opinion" word then the same must surely be true of ugly. But apparently the rules are different...
In short, what OP is missing is that "order of adjectives" is a complex issue. But note that doesn't mean "different grammars" disagree about what's correct (these days, "correct" just means "most common").
The reality is actual native speakers tend to be consistent about the order they prefer for any given set of adjectives, but grammarians/linguists struggle to describe/define those preferences in a way that would enable non-native speakers to predict what form the natives will choose (i.e. - formal "rules").
But OP should also note that not all sets of adjectives will be consistently sequenced the same way by all native speakers (a point I hope the above two charts encapsulate, as well as showing change over time).
As a native speaker, I know instinctively which of these sequences is "normal", but the rules don't help...
big fat ugly woman 52 results in Google Books
big ugly fat woman 1 result
ugly big fat woman no results
ugly fat big woman no results
fat big ugly woman no results
fat ugly big woman no results
In short, it's probably worth learners taking note of the basic sequence...
1: number
2: judgement/attitude
3: size, length, height
4: age
5: colour
6: origin
7: material
8: purpose
...but you've only got to look at the comments against the ELU question and answers to see that it doesn't work in every case (and things get particularly imprecise around category #2 above).
Best Answer
Please see “My personal opinion is…” Is it always pointless to use the words “personal” and “personally”? on English Language & Usage.
From @JoeZ's answer:
From @andy256's answer:
Personal can be used…