ZhuangZi, the ancient Taoist philosopher, wrote about this thing he called "this-yes". To a fish, the fish is this (as opposed to that). To a fish, water is yes (as opposed to air being no). The fish lives its life following along the this-yes of its situation. ZhaungZi's point here is to demonstrate that, although the lines can be drawn somewhat arbitrarily, every person, plant, animal, and even inanimate object has a "this-yes" to it. Of course, there is also a "that-no" of everything.
(Side note: combining the two is how we get to the Tao. For example, the "this-yes" and "that-no" of a cat taken as a whole could be called the Tao of the cat. The entire universe, taken as a single cosmic entity, has a "this-yes" and a "that-no". This is what the capital-T Tao represents, and it's also what the yin-yang symbol represents.)
The point I want to make here is that Based and Cringe are just our new words for "this-yes" and "that-no", respectively.
Given a "this-yes", there is only one "that-no" to go with it. In this sense, cringe isn't so arbitrary at all. As long as it goes against the "this-yes" of the observer, it's cringe. I think you will agree that society and the internet do a great job at homogenizing homo sapiens. The CIA's researched this, and they found that there's only like 8-12 groups (I can't remember the exact number they found) people fall in. Everyone's in one of those, more or less, which really isn't a lot of variety. In other words, one person's "this-yes" is rarely just their own, most of the time it's shared with the people they hang around, or their community at large, if there's enough of em.
This is to say that cringe (and based, by extension) aren't completely arbitrary terms. Yes, they can vary from person to person, but not without rhyme or reason, and more often then not, if a community shares a "this-yes", it's practically an objective matter.