The Continuum hypothesis is independent of ZFC. It is the first of Hilbert's 23 problems.
The CH is undoubtedly meaningful, natural, and of huge interest to (a subset of) mathematicians.
There are huge branches of mathematics that don't find immediate practicality in physics. Often these end up being practical in cryptography or quantum mechanics, but sometimes they don't. But to dismiss the entire field that relates to the cardinality of real numbers as uninteresting if someone can't give you a practical application of it shows a simple disregard for other fields of study.