Even time travel shenanigans would be a more likely explanation

Not that anyone isn't allowed to not enjoy Stargate, but maybe this will help:

I'm an embarrassingly hardcore sci-fi fan, and it even took me a little to get into SG-1 and beyond (SG Universe is a separate...argument lol) and I'd seen occasional SG episodes as it was airing, and was even living on Cheyenne mountain at that time, so there was a fun "connection", but it didn't click with me, it was just confusing and silly and I was all about Star Trek and book learnin'.

However, it wasn't until the beginning of the pandemic that I sat down with it, with a very open mind, and later pulled it up as a re-watch when I worked through my comfort re-runs of everything else.

Upon a second watch through, and learning about it via companion trivia reading with the episodes, I fell for it, pretty hard.

Now, I work with some official ST stuff, and I'm frankly disheartened and bored by a lot of it. But I've never gotten that with Stargate. It's my constant companion, and my spouse and I find more and more to love and laugh about and enjoy with each episode our dumb asses will watch over and over again.

It's, uh, rough in the very beginning. It got so much better once they switched to Sci-Fi Channel, which is amusing really, and it just got better and better. It's full of callbacks and continuity, referenced goofs, and chemistry that is unparalleled. SG: Atlantis is a fun journey, too, with a great cast, but it took a much larger ensemble to amass anything near the connection that the central 4 have in SG-1. Even when their roll of greatness slowed a bit, in the ending seasons, which like ST:DS9, has a disturbingly timely enemy, they took the stars of Farscape, and Ben Browder slid right in to playing Ben Browder in every role, and Claudia Black 180°s to something bizarrely hilarious when compared to her usual stoicism as Aeryn Sun (I'm 1,000% convinced anyone that is strongly against their casting hasn't seen Farscape, or doesn't understand campy humor, at all, haha).

The last above being said, enjoying, or learning to enjoy campy humor is pivotal for enjoying and understanding Stargate, I feel, anyhow. I probably didn't connect with it when it was airing because I preferred deep and dark, I was just getting into reading Frank Herbert, and my depression was kicking my ass. I couldn't have even understood its levity, at the time, let alone cared for it. Too silly, how dare they! But now? Especially knowing it was made...then? It's just phenomenal.

Like most recommendations for a TNG era Star Trek series, "Keep watching! It gets good in Season 3!" but really, it all has good, (minus that eerily same misogynistic episode like Code of Honor, ALSO written by Katherine Powers), but I promise you, it's worth it.

The portrayal of sexism that Samantha Carter and other female military members face is actually an overall positive part of the shows writing. They highlight how problematic it is and Dr. Samantha Carter continues to rise through the ranks as her accomplishments are recognized by the good leadership that she serves with. She is far from a token character and she provides some of the most significant contributions to the team.

So that issue you have does get better. I would argue that the writing overall is rather progressive for the time.

Feel free to not like the show though. It can be a bit hokey. Not everyone enjoys cheesy sci-fi.

I watched SG1 as a comfort show with my partner, and I am glad I did. I am glad I know the references and have experienced the 'gems'. I am often amused at some of the bad parts, but not always.

Many of the bad parts were SO bad that I'd never watch it again, and I wouldn't recommend you spend your time on this when you already discovered that the bad parts grate this much. Life is short and there's a lot of other things to experience.

I think if youve watched some episodes in s1 (which it sounds like you have) feel free to skip to s3 or 4. The story becomes a lot more focused and they find their groove more. After that it just keeps getting better. :)

You don't have to like everything. Stop forcing yourself to watch something that you don't like

Given that you have already received some replies which I largely agree with I'm going to focus on some of the specific points of critique you raised.

The mystery and intrigue gets overshadowed by sexism,

I mean I can't really say that this isn't portrayed in the show, especially in the first few episodes, but I can't recall any instance of it being portrayed as a good thing. Quite the contrary actually.

jingoism,

The show is indeed rather militaristic, but given that the antagonists are a species of parasitic aliens with a god-complex

spoiler

(a plot point which gains more nuance in later seasons as well by the way)

I always saw this as a thinly veiled metaphor for armed resistance against the divine right of kings. So I wouldn't go quite so far as to call it jingoistic, although overtly militaristic is certainly a fair assessment.

characters that can be summed up on a postage stamp

As you already surmised this gets fleshed out a bit more later on, but stays more or less the same. Most characters, certainly the main cast in any case, stay rather archetypical with some character development happening though.

and plots and scenes that are contrived and clumsy.

This happens throughout the entire series unfortunately, but it varies a lot from episode to episode rather than from season to season. There are some rather interesting interpretations of common and uncommon sci-fi tropes throughout as well.

do they ever solve how the female token character is being treated?

Since you didn't exactly point out your problem with her portrayal I can only guess what you mean, but yes, I do think so. There are also other women joining the supporting cast (and even main cast in the last few seasons), leading to less frequent failure of the Bechdel test.

Does it ever stop feeling cheap and schlocky?

Not quite, but the first two seasons are certainly the worst in this regard, mixed in with most of the retconning happening to their content.

All that said, there is a reason the original show has 10 seasons at 22 episodes each, three movies, and four spin-offs, and if you can stomach early Star Trek TNG (or even TOS), you will probably enjoy at least the SG-1 series overall.

IMHO the first season is the weakest, second season is not great not terrible, 3-8 is the peak, 9, 10, and the two TV movies trail off a bit although still better than the first two seasons.

If you want to skip some seasons you should be aware that most of them have a "clip-show" episode towards the end that recaps the season and embeds them into the larger narrative happening in the background. I'd say the bad episodes are worth stomaching for the context though.

Atlantis spin-off is worth the watch if you liked SG-1 overall. Chronology is a bit weird though, SG-1 season 9 and 10 and Atlantis season 1 and 2 overlap.

Universe spin-off you can skip unless you got really invested.

spoiler

Universe ends without wrapping up its underlying narrative in any way since the show got canceled.

Haven't watched the animated spin-off, Origins was meh.

In conclusion, it's probably worth giving it a shot if you can manage to not take it too seriously.

At least in the few episodes I've watched it feels like they are doing it at any point something is being discussed or vocabulary is being used that exceeds that of a fourth grader. The impression is that they aren't taking their audience seriously at all.