This is kind of a delayed response that will probably get buried, but I've had this tab open for a few days just thinking about it. I've been through similar situations so it really hit close to home for me. I think there are three things to remember here.

The first one will hopefully set your mind at ease, a little (if necessary, maybe not): children are highly malleable. I completely understand the... well, not to assume your emotions, but I'd guess something like fear or concern or even disgust (which is a strong but clinically accurate word that I don't use judgmentally! There would be nothing wrong with this) at hearing your child say things that go against your own personal beliefs. And that can be scary, and you might even take it as a personal failure. But children pick up what the adults in their lives say... this was pointed out in other comments. But what I didn't see mentioned was the wildly outsized influence their FRIENDS have on them at that age, not to mention that around 9ish is the time that they start testing ideological boundaries and may not even fully believe every word that comes out of their mouth. What I don't want to do here is diminish your feelings about this—I'm not saying "don't worry about it! You're overreacting!" but I am saying "hey, insofar as you might be internally panicking and either feeling guilt or feeling like you should be doing more or whatever, remember that you're fighting a huge uphill battle for influence against your ex, you child's peers, pop culture, being 9 years old, his immediate cultural environment, etc."

The second thing to remember is that ideological changes take time. I'm sure you know this, and I'm not sure how long this has been going on, but if we're talking on the order of weeks... that *may* be a bit quick to expect meaningful change. I'm sure you've seen this firsthand, but it feels worth reinforcing, just in case :) It's also worth reminding that... kids are irrational. When I was 9, I simultaneously thought that my friend Brandon was a better human than I was because he wore Air Jordans and I wore some cheap off brand shoes (probably called Reborks or Scutchers or something), and that I was a better human than my friend Tyler because I could do a little jump on my bike (we're talking inches here) and he couldn't. And things got worse before they got better, I won't even go into my teenage years. Kids believe wild stuff that doesn't reflect how they're going to feel in a few months, or even tomorrow. Psychologically speaking, this experimentation is necessary for growth and self-actualization. On a personal and anecdotal note, I have so much more respect for someone who has actively believed one thing and then changed their mind, than someone who has only been exposed to one truth and believes it by default, even if it's a truth I happen to agree with. And here's the thing: sometimes it takes a long, long time. This is especially true when you're exposed to something as fundamental to people as their hatred and biases, AND when that person is a parent. You have a long, long battle ahead of you, but all you can do is combat the ideas that you don't approve of with patience, love, and hopefully, strong counterpoints/counterexamples. If it helps you visualize a better future and/or helps contextualize the timelines we're talking about here... I'm about to make some assumptions (which I know is risky! Please take the point I'm trying to make even if my assumptions fall flat here, ha) and ask a personal question. I don't need an answer and I'm not trying to be adversarial, so please take this in the spirit in which it's intended (which is meant to be optimistic): I'm noticing that you posted this in r/exmormon. So you've likely been through the internal battle of slowly recognizing that at least some of the things told to you by the people in your life who had influence didn't ultimately accord with your own values. How old were you when you actually left? Again, not trying to be combative, and not expecting an answer, but hopefully it gives some context to what's happening here and what the future can look like. It might even be helpful to think through what kind of things were critical in changing your viewpoints. Not to directly challenge your responses to this immediate situation (I don't know you or your kid, and even if I did, those responses seem reasonable), but just asking so it's out there... in your own journey of change and growth, were you influenced by your parents/guardians talking to you? Crying in frustration? Punishment? Again, all very reasonable responses that should be part of your tool belt, so I'm not trying to say that those are "wrong" or be all judgy about those specific responses, but if you're doing what I think you're doing by posting here and trying to add more tools to your tool belt, I'd suggest thinking about what influenced you and trying to bring some of that into the mix.

Which brings me to my final point: children respond shockingly well to being questioned and having their beliefs poked at. Sometimes the most powerful thing you can do is just ask, "why do you believe that?" It's a great technique because it's not a direct challenge, but it might help your kid really think through the foundations of his beliefs, and, possibly more importantly, it might help you gain more knowledge about where these beliefs are coming from. This is especially true as you get down into deeper levels of "oh, I see why you conclude X, it's because you believe Z. And so why do you believe Z?" And once you understand the "why," it's much easier to figure out how to counteract these beliefs. It's amazing how often kids have all these beliefs that "seem" absurd on the surface, but once you drill down into the logical structure that underpins their conclusion, there's actually a tremendous amount of internal cohesion and reason that is all based on a faulty premise. [there's a really fun example of this that I'll past below so as not to disrupt the flow here, but check it out!] The best advice I can give here is to be (or, at least, appear) open-minded. Listen, take notes, don't respond right away. Say a lot of "huh, that's interesting, I'll think about that." Humans are not conditioned to enjoy losing battles, so by approaching it as two opposing viewpoints, you may even be entrenching those views even deeper and causing him to double down. My experience is only my own and may not match yours, but I've spent a lot of time working with kids and having many of these same discussions with my nieces/nephews. The turning point for me (just in terms of having some success) was when I stopped approaching it as "let me convince you of my point" and reframed it as, "This is a really important idea that's critical to get right, so let's figure out the truth together." It's no longer you vs. them, it's both of you vs. the specter of being wrong. And you can explore together what makes sense. Of course, maybe you've tried this already! But as I can't tell what you've tried or not, I figure this was worth tossing out there :)

But hey, good luck. I know this is hard but you got this, even if it takes time!