Not a fan of certain tags such as BL, NTR or futa, but I can filter those out, and they're only a moderately strong signal that I'll dislike the work.
The synopsis by itself is usually more than sufficient. It tells me a lot about the writer, and thus the work. These are my personal red flags:
The main thing is SPAG - when the synopsis (or god forbid, the title) is written with noticeably bad grammar, has missing punctuation, capitalizes random words, etc.
Imagine: You've spent hours (I hope) of your life writing a story. You get to write a summary of your work, something to draw readers in, the first thing any potential reader will see. Shouldn't you make sure that at the very least
that looks readable? Apparently not. It's bewildering how many of them are so bad - like the author is completely unfamiliar with concepts such as spellchecking, thinking before you write something, double checking your work, googling unfamiliar words, this little thing called "editing". I know for a fact that even ESL children can write better, so neither is an excuse - not that you should ever admit you're underage on the internet.
The first sentence linking to a discord or begging the reader to do or not do things is annoying, as are most similar meta warnings. Unless it's warning me about prequel/sequel information or part of the work being missing, that's what the genre and tags are for. Also, when searching, only the first few sentences are visible without clicking on "more>>" - take advantage of that. Put everything that doesn't describe the actual story at the end.
The whole synopsis being a character talking about how he/she got isekai'd is weird and off-putting. Trying to be flowery and poetic can succeed, but usually doesn't. Talking like you're an anime character is insufferable. Addressing the readers directly can sound very narcissistic if you assume they'll love your work, and even if you don't.
But honestly, I can take all those, as long as it has capitalization and periods, and gets its/it's right. Often it doesn't.
After all of that is taken care of: You need something interesting. You need characters with clear motivations, a good premise/scenario, and some kind of conflict, ideally. The synopsis should give the reader a hint of what's to come. It's not a tl;dr of your first chapter. "John McExample was bullied, died, then the Goddess of Only Appearing in One Chapter sent him into Instant Harem World." Why? And why care for John McExample? What problems will he face?
I've observed that usually these kinds of problems cooccur with some others that you can truly call "red flags":
- Ellipses with more than 3 dots (......)
- More than two exclamation marks!!!
- A male protagonist being some kind of ex-military special forces Rambo dude.
- Mentioning real-life celebrities.
- Criticizing other stories/authors in your synopsis.
- Emphasis on the story being cold, dark, gritty, realistic, mature, etc.
- Using foreign character names without justification.
- Mentioning that the story is being rewritten.
I'm not sure why, but that list is on the money 99% of the time.
There's a lot more to say, but this reply is already too long.