At which point is it OK to slack off attack IV?

Personal standard - 15 or go home.
Practical standard - whatever is needed to reach BP of what it is specialising against

I never look into base stats, even while it makes more sense to do so. I power up based on what I feel makes most sense. Mostly, I'll prioritize the attack individual value (read: IV).

It depends on the attacker's base attack, the fast move's power, and the defender's defense.

I know that Raikou, for an extreme example, has a significant breakpoint for Thunder Shock against Kyogre raid boss that can not be reached with 12 or lower Atk IV.

I think big breakpoints that can't be reached with too low IVs are rare. Generally, for the most part, better IVs mean fewer power ups to hit breakpoints. Choosing a pokemon with 15 Atk IV though ensures that your pokemon will be able to hit any possible breakpoint available to it against future raids.

I mostly want 15atk (and good overall IVs (91+), but if I can't get that I'll settle for the next best thing. For example, I really wanted a Groudon but had to settle for a 14/14/12. It's not bad but it's not good either imo, but it was the best I had. Rayquaza on the other hand is not that much of an improvement compared to Dragonite, of which I have 4 (93%, 96%, 2x 100%) at 40 and 3 more at 35 (2x 98% and 100%), and therefore I want one that is at worst 15atk and 96%.

In short, it really depends on what Pokemon it is whether I boost ones that are in the top percentage or whether I settle for lower.

Just thinking loud:

If we take Gengar with SC. It has around 5-10% higher DPS than H. And we all are pretty unanimous that there is a clinical difference actually worth something.

If we consider attack 300, 200 and 100 as a bench mark.

comparing 15A vs 10A at 300,200, 100 base attack value:
Damage difference: 1,7%. 2,5% and 5%.

So there should be no to little noticeable difference in pure DPS with around 300 attack base stats.

But than there are break points, TDO, EPS, accessibility etc .

Gengar with a high Defense and Stamina can in some cases fire an extra Shadow ball. And SC has a high break point lvl for many raids meaning that a 98% IV can have an a lot higher DPS than an 91%.

Just thinking loud though.

Just get to the attack breakpoint and hopefully a relevant bulkpoint; that’s all that matters.

Depends on every single defender's defense stat and iv.

When it's a Pokémon that you can't reliably get outside of a Raid, it's okay to slack off on the IV's. Which means, essentially, that this only applies to Legendaries. (unless you're that guy who uses Absol or Mawile as an Attacker. If that's the case, Hi! You are a very confident person.)

For all other Pokémon, Attack 15 is the standard. There isn't a huge reason to slack off on the Attack IV unless there are clear individual reasons why. (ie: your area doesn't have many of a certain kind of Pokémon or not enough players to regularly do Level 4 raids, or just ridiculous bad luck) And that you need to have that Pokémon RIGHT NOW to use. (Which is almost exclusive to Tyranitar. Dragonite used to have that designation, but neither the way Gyms work nor the current Raiding system rewards Generalists like Dragonite, so it's usually better to go for Specialists.)

Other than that? There aren't many reasons to power up non-Attk 15 Pokémon. Not saying you can't - for instance, I've had extremely bad luck with Larvitars/Tyranitars and out of 16 hatched Larvitars and 8 caught Tyranitars from Raids, I have exactly 1 with Attk 15. (only 2 of them have IV's in the 90's, neither of which have Attk of higher than 13) Even after Evolving one from a Larvitar and powering 2 Raid Catches up to level 35, I currently have 177 Larvitar candies ready to go for when I hatch that awesome Larvitar and want to Evolve it and Power it up, but it hasn't come yet.

But I've been stockpiling for that high IV, Attk 15 Tyranitar that I know is coming... someday.

Look at it as an individual case for individual pokemon, in some cases 1 attack is enough in others its 15 or not enough. I would look at the pokemon you have and then work out the stardust to reach the final breakpoint against its speciality ie Machamp vs ttar. The one that is the lowest use

13, 14 or 15 in attack is in most cases rather marginal differences.

Only exception is when the Pokemon only have one single usage and you are struggling to succeed (like picking a Genger to be able to take out Alakazam-raids). Then it may pay off to look deep into stats and offensive and defensive breakpoints.

Other than that I do not care much.
IV >93 is more of a collectors item than a requirement for success.

Without thinking about moveset, SE, Weakness, etc

Generally i chose the best that i have, if its 100 iv then fine, if not 97 even with 14 atk is fine by me, and if i dont have it the next best thing is ok
I dont mind poweing the best that i have, if i get a better one, i power it up, so i have 2 good attacker..
And for me the most important thing is do i need it now for battle or not..
I even power up my 77 atk 10 Tyranitar till level 34 just to help me solo raid Gengar back in the day because i need it and dont wanna wait for a better one first to win vs gengar
So, yeah i will wait for a good one when i think i dont really need it and take my time. For example i am not power up all of my legendaries, cos i dont have a 100% one and my regular mons can still handle all the raid, either soloing tier 3 or group raid tier 4-5 ( when i raid with 5 trainer my personal damage is +3, and that is good enough for me)

I look at overall IV, not just attack. That 12A/15D/15S Larvitar that I hatched will be useful some day...when I get enough candies.

I assume you mean, “what is ok to invest a significant amount of dust and candy into”.
Otherwise, the question doesn’t make sense, if the mon has reached the final/necessary breakpoint when evolved even with low attack it really doesn’t matter i’m Gonna keep and use it as is. Additionally, a small investment <~15k-20K to achieve a significant breakpoint is worth it too.

But powering up many levels should be reserved for 14 or 15a only and ideally only 91+%.

But every now and again.....hey live a little