No, Chinese do not have a culture to have conflicting ideas and not feeling stressed, not as anything I know from my 24 years of living and studying as a native Chinese.

If you are talking about "求同存异" that's for agreeing to have disagreement, which is a common cooperation culture around the globe.

If you are talking about "无为而治" from the Taoism philosophy of doing without actually forcing, that's not something relevant here though.

PS: I am often amused by people coming up with obviously-weird/nonsensical claims on Chinese, China or its culture, and the readers seemingly unable to apply common sense to disapprove them. This, to me, is an unconscious (or actually intentional) way of reinforce stereotype on China, which can be useful, for example, in mwny cases when someone in power wants to mobilize the common people, such stereotype really makes things easier to get approved.

Being able to manage what seems to be multiple "conflicting" ideas at once and without stress should be prized in every culture.

The world is not black or white. Enlarging your perspectives always help.

Conflicting ideas means believing that princess Diana was murdered by MI6 and that she was kidnapped by another shadowy party. Or that migrants will simultaneously take all the jobs and that they all just come to leech our welfare system dry.

On a macro level it is absolutely possible for immigration to both depress wages and overburden the welfare system.

Fox news and CNN would beg to differ

Where have you heard this about Chinese culture in particular? I’ve only heard of such a trait in reading Robert Altemeyer’s book The Authoritarians, where it is described as a common trait of right wing authoritarians, who appear to not be very good about comparing the various ideas they have together to see if they are contradictory. Altemeyer describes it as the result of an upbringing that emphasizes loyalty and submission and that posits that truth is something that comes from an authority figure, rather than something that can be derived from available facts for oneself. But I think that applying that critique to an entire country seems harsh, without evidence.