Not really... That is a symptom, not the cause of the Chinese civil war(s). The arrival and the dominance of the Western powers eroded the strength and faith people had in the Qing Dynasty. The Taiping rebellion was a reaction to that but just one event in a long series of the fracturing of China as the Qing declined.
Christianity isn't being singled out. Islam is also a target. They oppress the hell out of the Uighurs too. (Although they do tolerate the Hui but the Hui have been in China for centuries and are generally assimilated)
They also targeted the Falun Gong.
As a rule of thumb, anything that represents an alternate source of authority in China will be targeted and oppressed.