The issue is that Anthropic is just one company and China doesn't care in the slightest - so it's an entirely moot point and almost narcissistic (on Anthropic's part) to believe that they can have any impact whatsoever on this situation.
But the question is conditional on them deciding to, which (to the extent you trust Anthropic leadership which they're probably also filtering for in interviews) is conditional on believing that a decision that sent their stock to 0 would have a real impact.
Spend 5 minutes with DeepSeek, spend 5 minutes with Fable, see how many rejections you get with DeepSeek for the exact same prompts. Sure, if you engineer some nuclear/biological/WMD prompt, they might block it, but they won't reason to do so.