Not only that, but you have to belong to the government approved branch of each of those religions, and have your specific beliefs subject to scrutiny and approval.
Except when you consider that any form of protest against this oppression is met with intimidation, if not outright violence.
I agree the first part is oppressive, but it's not militant. The second part isn't oppression against religion, it's oppression against protest. The Chinese government strikes out against protest because they've been able to retain a long memory of how they came to power themselves. They don't say "You can't worship this religion", they say "you can't worship this religion in a mass, if you must worship your religion en masse, do so at one of these holy centres, too bad if it doesn't fit all your criteria." You don't govern 80 trillion people and not disappoint a few.
Religion doesn't work that way - a religion is a holistic ideology that needs to be expressed and understood in its entirety. It is much greater than the sum of its parts which is why religion isn't able to be analysed piecemeal. Every part of it needs to be considered in context of the rest. This is why artistic and social thinkers have always had more success understanding religion than scientific minds have.
Therefore if you feel those people are perverting your religion, despite it being 'sort of' like your own then you're probably not going to feel comfortable experiencing their religion with them. In many ways it's similar to the uncanny valley of robotics, and why the hostilities within a religion can be more vicious than those between them.
And this is why religion is shite. Even similar religions can't sit down and discuss why there is a difference and whether or not one is incorrect. They simply shout "no you are going to hell." And going back to China, that at least have the foundations of sorting the mess out.
If every option leads to a bad outcome, you take the true option. That way even though it may be horrible circumstances, at least you have the truth