@matana one singular part of the lore is that the order is trying to summon god to the earth and use alessa as a vessel to "birth it" although it's not really a "birth" so much as it is alessa being the host (god rips out of her back in silent hill 1 and in silent hill 3 claudia becomes the host after heather rejects god and claudia physically turns into god).
there's still a decent amount of imagery regarding female reproduction but i always read it as silent hill preying on heather's fears/angst as a young woman nearing adulthood. somewhat similar to beverly in IT. it's not like the game has a message about women's rights or anything like that, just the town sinking into those fears. there's certainly not NEARLY as much as there is for angela in silent hill 2, who was raped by her father and killed him. there's an enemy called "abstract daddy" that looks like a guy fucking someone on a bed and a section of the game angela's in that has pistons shooting through holes everywhere. like that's 100% a "visceral metaphor for rape" but it's also not the whole point of the game. there's nothing that even comes close to that in SH3.
like i said, alessa "birthing" god is just one plot point, and i think it's probably done more for the horror factor and a cool story element rather than "hello my fellow gamers, we here at team silent are pro-choice!"
there's so much more to silent hill and just saying the whole game is some sort of allegory to abortion or something is extremely reductive, not to mention annoying. there's the town itself creating horrors based on the psyche of the person there in order to test their courage and/or aiding in carrying out their repentance, a LOT of religious/mythological iconography and parallels, the importance of children and the way them being abused/neglected has rippling and permanent effects, plenty of gray characters with varying degrees of evil or good that often have their own motives or theories on silent hill as well as the cult and what motivates them...
there's just so much to unpack. yes, heather literally pukes up ("aborts") the manifestation of god that was lurking inside of her and it looks like a gross fetus thing. and she like uses a coat hanger in a puzzle. that's literally it lol. meanwhile there's this lurking sub plot the whole time of a guardian of god watching over heather and making sure she's able to get from point a to point b as she is trying to avenge her father's death, who was killed by claudia, there's this strange detective guy that is hired by claudia to find you but then turns out to be a good guy and a dude named vincent who is pretty knowledgeable about the cult and helps heather find claudia... like seriously there's a reason i think it's one of the greatest games of all time and certainly in the top 5 horror games ever created... so when i see someone just say "oh yeah the game is all about women's rights" it's just annoying, like did they even play the game or are they just reading waaay too much into a single plot point and stretching it to the entire game so that they can feel good about a game dev aligning with their politics?