I'm very happy to see effective altruism community members write public posts about EA organizations, where they point out errors, discuss questionable choices, and ask hard questions. I'd like to see more cases where someone digs deeply into an org's work and writes about what they find; a simple "this checked out" or a "critical feedback that helps the org improve" are both good outcomes. Even a "this org is completely incompetent" is a good outcome: I'd rather orgs be competent of course, but in the cases where they aren't we want to know so we can explore alternatives.
When posting critical things publicly, however, unless it's very time-sensitive we should generally be letting orgs review a draft first. This allows the org to prepare a response if they want, which they can post right when your posts goes out, usually as a comment. It's very common that there are important additional details that you don't have as someone outside the org, and it's good for people to be able to review those details alongside your post. If you don't give the org a heads up they need to choose between:
Scrambling to respond as soon as possible, including working on weekends or after hours and potentially dropping other commitments, or
Accepting that with a late reply many people will see your post, some will downgrade their view of the org, and most will never see the follow-up.
Surprising them is to your advantage, if you consider this tactically, but within the community we're working towards the same goals: you're not trying to win a fight, you're trying to help us all get closer to the truth.
In general I think a week is a good amount of time to give for review. I often say something like "I was planning to publish this on Tuesday, but let me know if you'd like another day or two to review?" If a key person is out I think it's polite to wait a bit longer (and this likely gets you a more knowledgeable response) but if the org keeps trying to push the date out you've done your part and it's fine to say no.
Sometimes orgs will respond with requests for changes, or try to engage you in private back-and forth. While you're welcome to make edits in response to what you learn from them, you don't have an obligation to: it's fine to just say "I'm planning to publish this as-is, and I'd be happy to discuss your concerns publicly in the comments."
[EDIT: I'm not advocating this for cases where you're worried that the org will retaliate or otherwise behave badly if you give them advance warning, or for cases where you've had a bad experience with an org and don't want any further interaction. For example, I expect Curzi didn't give Leverage an opportunity to prepare a response to My Experience with Leverage Research, and that's fine.]
For orgs, when someone does do this it's good to thank them in your response. Not only is it polite to acknowledge it when someone does you a favor, it also helps remind people that sharing drafts is good practice.
As a positive example, I think the recent critical post, Why I don't agree with HLI's estimate of household spillovers from therapy handled this well: if James had published that publicly on a Sunday night with no warning then HLI would have been scrambling to put together a response. Instead, James shared it in advance and we got a much more detailed response from HLI, published at the same time as the rest of the piece, which was really helpful for outsiders trying to make sense of the situation.
The biggest risk here, as Ben points out, is that faced with the burden of sharing a draft and waiting for a response some good posts won't happen. To some people this sounds a bit silly (if you have something important to say and it's not time sensitive is it really so bad to send a draft and set a reminder to publish in a bit?) but not to me. I think this depends a lot on how people's brains work, but for some of us a short (or no!) gap between writing and publishing is an incredibly strong motivator. I'm writing this post in one sitting, and while I think I'd still be able to write it up if I knew I had to wait a week I know from experience this isn't always the case. This is a strong reason to keep reviews low-friction: orgs should not be guilting people into making changes, or (in the typical case) pushing for more time. Even if the process is as frictionless as possible, there's the unavoidable issue of delay being unpleasant, and I expect this norm does lose us a few good posts. Given how stressful it is to rush out responses, however, and the lower quality of such responses, I think it's a good norm on balance.