Enforce? No.
Encourage? Absolutely.
Let me quote from a very important document that governs how our site is run — and how it should be run when we forget:
Be welcoming, be patient, and assume good intentions. […]
Language likely to offend or alienate individuals or groups based on race, gender, sexual orientation, religion, etc. will not be tolerated. At all. (Those are just a few examples; when in doubt, just don't.)
[…]
We're proud to be a large, user-driven space on the internet where name-calling, harassment, and other online nastiness are almost non-existent. It's up to all of us to keep it that way.
In summary, have fun, and be good to each other.
That's from Be Nice, our policy on acceptable behaviour on the site.
Be Nice is usually invoked when someone is doing something wrong, but that's not its only purpose, just the most common time we remind people about it. Be Nice is also, at its core, an aspirational statement about who this site is for.
We don't have that policy of what's okay only to stop people who don't follow it — we have that policy also because it describes who we are and want to be.
And who is that? Everyone. And how does it say we achieve that? By including everyone, and requiring that everyone be included.
How is that relevant here? Because as a community, the RPG community is really, really bad at including women and girls as fully-fledged members.
And as we all know, words are important — things like game rules can turn on a single word. How we use words on the site reflects who we are, and who we welcome, and how well we accomlish that.
Words have power. So that's why people raise things like using default “he” as an issue — because that word choice has power, in a way that practically and directly impacts the core mission of our site.
The wider RPG community has a poor gender record
The roleplaying games community has a bit of a gender problem, in that girls and women are generally not noticed, ignored, minimised, or otherwise not included when we talk about RPG fans. The image of RPG fans is generally male — and that's self-perpetuating.
Our policy on inclusiveness seeks to amend that, but preventing people from being mean isn't enough. People who are traditionally put on the “outside” looking in — like girls and women have been in the RPG community — need to be actively shown that they're welcome in order to overcome the barrier that past (and ongoing, elsewhere) exclusion created. It's not enough to be neutral — as the document says, we have to be welcoming.
We have to create that welcoming atmosphere on our site, and being a site made out of words, we do that with our words.
A side trek: Grammatical correctness is a red herring
Grammatical correctness is a red herring. There are many things which are grammatically correct which do merit changing a post. Being grammatically correct is not the minimum bar for quality here — far from it! Grammatically incorrect posts are generally just fine, and are sometimes fixed up, but we have no rule about requiring it. Conversely, we do have rules that require fixing up a post when it crosses certain lines.
Am I saying that using “he” as a default is crossing a line? No — maybe it is, maybe it isn't, but that's not the point this section is making. The point here is that grammatical correctness is utterly irrelevant in discussions like this about how we govern ourselves as a community. Defending something because it's “grammatically correct” is at best a misunderstanding of what's important to the site.
A further historical side trek: Default Masculine is neither grammatically correct nor incorrect
Believing that default masculine is the correct English grammar is actually a relatively new invention. It was created in the 19th century by England grammarians specifically to attempt to make it incorrect to use singular “they” for entities in a sentence of unknown (grammatical) gender. (Yes, that's right! Singular “they” is older than the default-masculine rule, dating at least to the 1700s, and obviously likely earlier too.) The official reason they did it is what we now recognise as stupid reasons: because “they” has weird number-agreement, grammatically. (This is a stupid reason because singular “you” has the exact same number-agreement dynamic — and a well-documented potential replacement in “thou” — yet they saw no need to “fix” that pronoun.)
So masculine default has no special historical or grammatical weight that makes it more correct, and the Victorian and Georgian grammarians who falsely taught that it did (along with other invented “rules”) were engaging in language revisionism that still causes problems today.
(Side-trek ended.)
What we should do
As I said, we encourage everyone to feel welcome here. And we require that people assume good faith.
So when someone in good faith proposes that a post's writing is reinforcing the perception that we, the RPG.se community, consider men to be the default RPG audience, through transforming gender-unknown subjects into masculine subjects, we should in good faith listen to that critique of the writing.
When possible, we should strive to show that we are actively including people who are generally given a harder row to hoe in our community, and we can do that in such small ways as correcting unnecessary re-gendering. (Or mis-gendering! We not only get unknown genders transformed into ‘he’s, I've seen even female characters in questions transformed into men by the answers.) We can rearrange sentences to not need a pronoun. We can use “he or she” or “she or he” or singular “they”. We can do like some RPG texts do and use default-she for GMs and default-he for players. We can alternate, looking at what's already on the page and choosing the other pronoun to balance.
(And if we do enough of that, the occasional default-he becomes better: just another stylistic choice among many, instead of the most common default used on the site. Doing more to avoid default-he means, paradoxically, that we don't even have to strive for some kind of perfection of non-masculine writing — which would go right past inclusive and comes back around to excluding some people.)
We can, in short, approach this thoughtfully and with consideration. We can show that we're making an effort, and not just dismissing or ignoring.
Should this be enforced?
Like I said at the beginning, no, this shouldn't be enforced. We don't need a mandate, just a shared aspiration.
We want to imagine that girl or woman reading a particular post and feel like they can see themselves in our writing, even if only because the writing doesn't assume they're a boy or man. Some of us are that girl or woman who wants to see us included in the site's writing! (That should go without saying, but sadly it still needs saying.)
It should not be enforced. It should be encouraged.
And I encourage each and every one of us to help in our own small ways, as authors and editors. I encourage everyone to be part of welcoming everyone. We have our small powers granted by the site, and we can use them for the betterment of this site for all our community.
Not just for girls and women
Although “he or she” is what prompted this meta, and so I address that specifically throughout, the principles I talk about are much more general and making girls and women feel welcome is just a specific application thereof. I'm a bit uncomfortable making this an endnote, but I'm not sure how best to convey that earlier or throughout while addressing the actual situation at hand.
I would hope that it's obvious how this applies to all people though. If not — focus on the principles underlying the answer. …Or tell me how to fix it. :)