China

In the USA, while there is on paper separation of church and state, in practice there isn't, because theists can control the state, and so they will just make up fake justifications for their religious laws they don't believe in themselves. The only way to genuinely separate church and state is to not allow theists to control the state. Legally, the CPC controls the state, and you cannot join the CPC is you are a theist, so you will be limited in any sort of political ambitions.

Proselytizing is also illegal. If people come to your church it should because of their own personal interests or for family reasons because of your heritage. It shouldn't be because some charlatan convinces you on the street or the television that you need to attend, because that just opens the way for a lot of exploitation, like snake oil salesmen and generally people who do harm to society at large.

If you are fine with those conditions, there are churches in China of many different faiths. The people who cry about persecution are often Christians who don't like these conditions, they want to be able to control the state like in the US and they want to be able to proselytize and can't. These are the evangelical types which definitely get persecuted in China but that's a good thing.

Evangelical churches are forbidden from practicing. However, China has no problem with orthodox(not even supresed during the Boxer movement, thanks to Russia not fucking over China nad having good relations with it for decades at that time), apostolic(entered via silk road), its two national lutheran(formed during the 100 years of humiliation as a countermovement to the colonialist churches of the western powers), anglican and even the catholic church. Don't be a prosperity gospel preaching, proselytizing, US goon and China is fine with your christian denomination.

So yeah, some christian denominations are persecuted. The vast mayority is not.

The American interpretation of "Freedom of Religion" is very broad and liberal to such an extent as to allow actual cults to operate freely.

In countries with common sense, all forms of religions and beliefs have to abide by the laws and must not disrupt the harmony of society.

Based if true but sadly Mormonism is growing there

I'm assuming that notion is based on primarily proselytizing missionaries. Some of the Qing emperors flip flopped on allowing missionaries (foreigners) to do their evangelizing (so, if the "China persecutes Christians" is some anti-communist "commies oppressing freedom of religion!" angle then yes that's a lie or at least an exaggeration, because China's relationship with religions - in general and not just Christianity - has a ton of history. Also see other replies on the permitted Christian sects list in other comments regarding today's PRC). In more recent/modern history (may fourth movement known for anti-imperialism etc) that missionary stuff is seen by some as a foothold for colonizers, but also during the Republican era missionaries were sometimes allowed in (think Pearl S Buck's family) and were also faced with getting kicked out later as the tides changed.

No, unfortunately not - Just kidding, I'm sorry, it's just that I'm Brazilian and we're going through some problems with Christians here in my country, in fact the world is going through a problem with Christians helping to pass anti-LGBTQIAPN+ laws.

Usually what is reported to us Westerners as "religious persecution" is the fight against terrorism and fundamentalist sects.

The Pope ordains a bishop in China. There are Catholic, Protestant and Orthodox churches in China and masses are said in more than one language because the population is so diverse. There are also mosques and Buddhist temples. But most of the population idolizes regional deities - probably because of the low belief in monotheistic religions it is categorized as a society of atheists - but religiosity is discouraged among members of the Communist Party of China to avoid conflict of interest. Historically, China has had a problem with monotheistic faiths trying to impose themselves by force on the population. Confucianism isn't exactly a religion, it's something that the CCP's relationship with has changed over the years.

Now, there are things that are forbidden.

A Protestant church that makes the faithful vote for a certain political candidate, sucks all the money out of its followers and spreads disinformation will probably be barred if it tries to open a branch there - very specific? I'm talking about religious leaders in my country.

Unfortunately, socialism has never succeeded in doing away with religion. There was religion in the USSR, there is religion in China, Vietnam, Laos and North Korea - Kim Il-sung was even born into a Protestant family - there are churches in all these countries.

Church in China

Church in China

I remember before you could use the internet to look up that there are 44 million openly Christian Christians in addition to mega churches and century old churches, a popular lie I heard constantly in the US was that China only had underground churches and all the Christians were scared to goto jail if they were caught.