I'm a practicing lawyer who took the LSAT years ago and did just fine. The vast majority of the thing is completely apolitical and simply tests analytical ability. Schools don't ask students to identify themselves by their political persuasion, so they really don't even have the ability to exclude applicants on that basis.
The truth is that more libs are attracted to the law, and conservatives are more attracted to business. That's why we see see such a disparity.
There's no question that most law school faculties tilt to the left, even at supposedly conservative schools. But that only matters after you get in. That's while the title of the article is so misleading.