Not sure why that's sinas chinam. It can just as easily be bias or stubbornness. Sinas chinam would be hating a fellow religious jew. I can think of many groups of jews that have criticisms on other groups but do not hate them. And some of those criticisms would be called by many others absurd.
Basically, Cbc thinks chabad is crazy and views them through that prism.
Dismissing thousands of yidden as "crazy"? Bias but not "sinas chinam".
Calling an established minhag Yisrael - which, need I remind you, Torah hi - a breach of halacha? Stubbornness, not "sinas chinam"
Being mevazeh a Talmid chacham berabim? Oh that is just CBC being CBC, no baseless sinah there.
You'll notice that in this very thread and in numerous others there is loads of questioning Chabad custom. How many got branded a soneh Yisrael?
One need not read through all the texts provided about this custom, the answer to the question is right there on the very first line. Literally. I've heard countless claims and accusations against Lubavitch. Never heard of Tehillim after davenning being an issue.
While it's generous of you to be melamed zchus, the prism I see is denigrating g'dolei Yisroel and generations of ehrliche Yidden based on nothing. That seems to me to be the very definition of sinas chinam.
I barely ever answer CBC seriously, it's almost always jokes from me - for the reasons @ExGingi mentioned. But you wanted to know why some would find his "biased prism" hateful, so here is a look into one instance, without delving into his post history.
There is a story I heard about a kindergarten aged child of Rabbi Slavaticki in Antwerp, and I don't know how true it is nor do I care. A non-Chabad classmate said to her, "my father doesn't like your Rebbe." To which she responded, "But my Rebbe loves your father."