I strongly oppose this rule and supporting this standard in any way as staff. So I'm mostly agreed with the proposal. Everything below is written under the (possibly incorrect) assumption that this change will be implemented. Read with that in mind.
I completely agree with Cimmerian above. I also agree with Roget. However, I think they're getting at different things.
So I would counter-suggest the following:
Change the Site Rules wording to:
Formerly, upvoting your own article was against the Site Rules. However, you are now free to upvote your article (or not) as you wish. This note is included only to clear up possible confusion. For more information, see How To Write An SCP (link).
The reason is that people can still cite the "advisory not-rule" as a rule because it's still in Site Rules, which means they can still use it as a content-free way to bang on newbies.
Then, add a longer explanation to How To Write An SCP. I suggest the following, though it could be pared down:
Upvoting your own article: You can upvote or even downvote your article as you like. Keep in mind that your vote will be ignored to determine article deletion. Also keep in mind that this used to be against the rules, so you may get negative comments from other users who are working off of outdated information. But it's up to you.
We also need to ask people to stop making comments based solely on downvotes, because it is, and always has been, backseat modding, and now the rule doesn't exist. We should probably make a thread announcing that general request, and update the Criticism Policy accordingly. And people who post to say they're downvoting based on the self-upvote, and nothing else, should be asked to stop.
The goal here is partially less shit-crit. It's our responsibility as staff to tamp down on shit-crit, so allowing people to continue to enforce a now non-existent rule would just be… a pretty bad idea.
And also because self-upvoting should not be bad business. It's totally meaningless and harms nothing and no one. We're trained to be irritated by it (including me) because it's been a rule for so long, and it's one of the main things we can't stop people from doing, no matter how much we try to make them. But the real root of the frustration is the rule itself, not the actual act of self-upvoting.
To address the only possible issue I can think of: Since we already check for upvotes based on deleted accounts when an article is borderline, vote-wise, there's no reason we can't also check for author self-upvotes to omit them from deletion votes. (Otherwise, see alternative suggestion below.)
YET ANOTHER ALTERNATIVE:
We don't actually need to discount for self-upvoting, the way we do for deleted accounts. If an article is close enough that it's saved from deletion by one self-upvote, then to be frank, there's nothing wrong with it being saved. If our userbase numbers start dropping again, then we can change this back, but for now, why make ourselves do extra work?
In that case, my suggested explanation in How To Write An SCP would read like:
Upvoting your own article: You can upvote or even downvote your article as you like. Keep in mind that this used to be against the rules, so you may get negative comments from other users who are working off of outdated information. But it's up to you.
EDIT:
I should clarify something, I just realized after re-reading this. I obviously hate this rule, but I don't at all fault frustrated vets for (accidentally) backseat-modding about it.
So I would also request that staff be nice to people who mess up and yell at people for self-upvoting. Just be clear it's incorrect feedback.
Because people who've given this feedback have essentially been trying to help staff, and this particular kind of backseat modding has such a long-standing tradition that I bet most of staff and vets alike don't even think of it as backseat modding (even though it is). They think of it in the same way as they think of correcting format problems. They're incorrect, but we've all fallen into that trap over the years.