No, I don't think so. Maybe I'm a bit paranoid but I tend to avoid software from Chinese companies because of all recent stories of a apps stealing/sending data that they don't necessarily need to function. But I suppose software from any country could do the same thing though...
Only in the same vein as the more extreme example of avoiding flight itineraries with a layover in North Korea is.
There are two sides to any story and countries have different versions of reality that they believe in and promote. Nonetheless it's foolhardy to not notice which countries take an overly keen interest in people's communications and the "correctness" of their views... and jail those saying things they don't like.
If you're completely unfamiliar with the history of recent Chinese-western software collaborations, try googling "TOM-Skype"
That seems like splitting hairs to me. Would you want people to reject your software just because of your nationality or that of your company? Probably not. So it seems to me that an implication of the golden rule is that we shouldn't do that.
I would understand if people from another country did not use my software for fear of an NSA backdoor. It'd suck, but I would not think twice about their decision.
On the jurisdiction in which I, or the company employing me, operates? That can well be legitimate. You're discriminating against the laws (or unwritten government policies) in that jurisdiction, not against people.
I think it's just that the investment firm who bought Opera also owns Qihoo 360, a notoriously sketchy “antivirus” (and I use the term loosely) company. There's probably nothing to worry about, given that Qihoo doesn't actually own Opera.
That said, I think a general lack of trust toward the PRC is understandable.