Let's say that it means loyal to a political party. The Democrats I know value qualities like compassion, honesty, tolerance, etc. more than they value loyalty to the Party. Republicans, on the other hand, at the present time value loyalty to the Party/Trump more than they value compassion, honesty, tolerance, etc. and more than they value democracy itself.
Saying that there are hyper-partisan leftists and righties now is sort of like saying that there are hyper-partisan law enforcement officials and hyper-partisan mobsters. Here in Oregon, for example, we have Republican members of our State Legislature who want to be exempted from the Measure passed by our citizens forbidding a member who has excessive absences from running again. There is no "hyper-partisan" left that wants the law enforced--there are only law-abiding citizens that want it enforced; but there ARE Republicans who want it ignored for THEM and them only.
I have never read Jacobin but from researching, it appears that the people involved might be considered hyper-ideological on the left of the political spectrum, rather than hyper-partisan. There certainly is a diversity of ideology on the left. On the right, it appears now that ideology doesn't even matter--just loyalty to one man. The GOP wants to replace every political appointee in the federal government with people who are loyal to Donald Trump. We are seeing people who were staunch "partisan" Republicans sounding the alarm that the GOP is different now. Saying that there is a hyper-partisan GOP is like saying Hitler was very conservative. There's just no comparison between people with extremely liberal ideas like (gasp) universal health care to people with ideas like taking orders from Putin, nullifying elections, killing Democratic leaders, criminalizing abortion, etc.
Fighting anti-democratic seditionists is not partisan, it is patriotic.
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