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.