I don't think China's stance on this issue has anything to do with religious beliefs. The Chinese polity never thinks in that framework. The way they think is quite simple, it's interest. In this case its broader geopolitics and their interests in Myanmar.
China had been struggling with getting cooperation from Myanmar for decades, only recently did China feel there is progress in the relationship with Myanmar due to a more open economic policy, thus it's doing all it can to maintain that rare opening. The past was actually nerve racking for China regarding this relationship, Myanmar was always implicitly threatening to allow US troops/special forces to be stationed there to counter China. From China's perspective this is unacceptable, it will not allow it to become part of the anti-China blockade. In this process of improving relations, China made many concessions to Myanmar. Many of Myanmar's policies have a negative impact on China's border region but it kept quiet to maintain the relationship and to not embarrass them internationally.
Now in comes the Rohyinga crisis, its something Chinese government really wants to resolve as Bangladesh is an important regional partner, this is a long standing fact. On the other hand if it shuns Myanmar and pushes it too far, China will be blockaded and will counter China with US presence, possibly shutting down the pipeline and killing Chinese business interests, this is unacceptable. Another point is that Myanmar boarders China, their internal stability (relative stability) is vital. Jihadists even if they are few, are not welcomed, they have a tendency of taking things too far if given power.
Perhaps China's way of brokering peace in the region doesn't release emotional tension in the short run but I think there is few other ways to maintain regional stability. There is past precedent where China's methods worked, many of the bordering region with China and Thailand is now settling down. Only after people stop the cycle of conflict can there be a real resolution and development but China can't apply too much pressure on Myanmar out of external factors (China is not a superpower).
I know this is a military forum but one essential element of China's rise is swallowing your pride and doing what is right for the long run for your society, even in the face of humiliation. From the 80-90s it abandoned its military, it stopped funding it and told them to find their own money, so that the government budget can be focused on growth. During that time China was humiliated many times geopolitically with crisis after crisis. 20 years later China has improved many times over and now has the capability to redevelop its military from a much larger budget base, more than it would have had if it stuck with a militaristic policy. To be honest I think Bangladesh is the country in the region with the best long term development policies, and spends little on its military. I understand in the short run people can feel insecure and weak but continue with a peaceful development for 20 years and you wont regret it.