It's MY press not YOUR press.
I'm sure this was sorted out for newspapers a very long time ago, and anyone serving web pages to the internet is a publisher every bit as much as a newspaper is. The publisher owns the computers generating the search results, and if freedom of speech means anything it means they have an absolute right to "print" anything they want, subject to overriding laws (on incitement, porn, etc.)
The judge is right. If you don't like Baidu, use a different search provider. If you don't like any of them and have enough money, write your own, thereby expressing your own freedon of speech. You might well start by generating a database of articles containing "China" "Chinese" "Sino-" etc. that can be accessed through Google but not through Baidu.
Paradox? What paradox?