China does not play ball, at all. Literally don't give a shit about the Wests opinions or approaches to deals. Perceived in the West as cheating, but that is just a cultural viewpoint.
WeChat could be a real threat to Google and Facebook. It's comprehensive; you can do messaging, banking, shopping, and taxi calling from inside WeChat. It has sub-applications for other services. It's a post-desktop world. Google and Facebook came from desktops and crammed down to phones; WeChat was born mobile.
[0] http://www.cnbc.com/2016/02/22/huawei-well-re-enter-us-marke...
Europe is pretty inflexible, compared to the US. E.g. there is no free market for most agricultural products in the EU. And before you say it, no this is not due to US meats having hormones in them. Firstly, those taxes and rules apply to everything, whether or not produced with EU rule compliance, and secondly, there isn't even a free market within the EU for many products (e.g. wine in France. Olive oil (or other oils) in Southern Europe, ...). And of course, the EU is certainly not neutral when it comes to other products as well, e.g. Boeing vs Airbus.
China is extremely INflexible and hostile to free trade, even today. VERY few commodities trade freely with China, even just taking the published import tariffs and conditions.
Add to that that the Chinese state famously owns pretty much every large Chinese corporation (state owned enterprises) and it's influence and restrictions over what products are welcome in China goes above and beyond the officially published rules.
So I believe a fair assumption would be that no, the US would not object too much to large Chinese companies being successful in the US. In fact, I do believe there's large scale examples of that if you search just a little bit.
For a practical example of the US allowing large non-US businesses to operate freely in the US, even where it hurts local industry, you only need to look at the steel industry.
Google and Facebook in particular are a security agencies dream - people volunteering to share messages, location, what they're reading, who they're friends with, etc - that a rational country would be afraid of from even friendly nations.