Warning: this post may contain spoilers
I watched Supernatural until season 7 or so when I was younger. I didn't really examine its subtext at the time, and just thought it lost steam after the original plot ended. I've recently started rewatching the show from the beginning, and, wow, like just wow. It's amazing how much Christian and Western supremacist subtext it contains.
Before I get into the details, I should mention that I've only rewatched the first five seasons yet. So I don't know if this still holds true after that. With that out of the way, here are the major reasons (obviously, spoilers).
Pagans are always depicted as bloodthirsty maniacs. Every single time.
Holy aspects of Christianity -such as exorcism rituals, churches, holy water- are the only "real" effective way of fighting demons. The other ways are made up in the show (demon killing guns and blades).
The cosmology is a thing on its own. Christian God has created the universe, yet Earth is at its metaphorical centre. Knowing a few things from the seasons after too, I can say that it's the only place of importance in the entire universe. Following the traditional Christian logic, humans are also the most important beings on Earth.
A special mention goes to the episode "Hammer of the Gods" (S05E19), as a striking example of what I talk about. In the episode, the major "pagan" gods alive gather to talk about the looming apocalypse. This includes Kali, Baldur, Mercury, Baron Samedi, Zao Shen, Odin, Ganesh. It's really telling that they threw in Ganesh and Kali together with old gods. Oh, and of course they all eat people.
The said apocalypse is to be caused by Lucifer coming back and fighting it out with Michael. Apparently it will be so bad that it will kill around half the human population.
The gods gather, conspire, with leads Dean and Sam there being held hostage as bargaining chips. They say they have to conspire, because if not prevented, this Christian apocalypse will kill them too. So this led to them teaming up. You can already see that Christianity is depicted as the big bad boy in the entire world.
During the talks, Kali says this to Loki, who she discovered was actually arcangel Gabriel.
"Westerners, I swear. The sheer arrogance. You think you're the only ones on earth? You pillage and you butcher in your God's name. But you're not the only religion, and he's not the only God. And now you think you can just rip the planet apart? You're wrong. There are billions of us. An we were here first. If anyone gets to end this world, it's me. I'm sorry. [KALI stabs GABRIEL with his own blade. GABRIEL screams, and in a flash of light, dies.]"
Don't worry he doesn't actually get killed by Kali.
Almost just after this scene, Dean gets up and says the following. Emphasis mine.
"All right you primitive screwheads, listen up. I'm outta options. Now on any other given day, I'd be doing my damndest to, uh, kill you. You filthy murdering chimps. But, uh, hey, desperate times. So even though I'd love nothing better than to slit your throats, you dicks, I'm gonna help you. I'm going to help you ice the devil. And then we can all get back to ganking each other, like normal. You want Lucifer, well, dude's not in the Yellow Pages. But me and Sam, we can get him here."
I swear, at this moment, I could almost see a 19th century colonizer white supremacist manifest to say this. I should remind that he says this to a group of gods that includes two major gods from Hinduism: a major religion that still exists. It would have been bad even without that, but this fact makes it much worse.
After this, Lucifer shows up, and kills every god with ease. He's not even the Christian god, and he's not even at his full power, yet he kills multiple major gods from other religions as if they were less than nothing. Oh, and he says that to them too.
"You know, I never understood you pagans, always fighting, always happy to sell out your own kind. No wonder you forfeited this planet to us. You are worse than humans. You're worse than demons. And yet you claim to be gods. [LUCIFER twists his fingers and MERCURY dies as his neck snaps] And they call me prideful."
He then kills Gabriel for real too. Because, as is tradition, gods from other religions are too incompetent to do anything to Christianity.
This episode is probably the epitome of what I mean, but it's just a culmination of what's been there from the start. The trashing of what is deemed as "pagan" (often read: not "Western"), and the supremacy of Christianity has always been there. I still like the show for its other aspects, but its subtext is really Christian and western supremacist.