Statisticians have a saying, “all models are wrong, some are useful”. What we have is that math is useful for modeling physics. But it is just that, a model in so far as we know. Believing that math or logic is intrinsic to the universe is not all necessary to using math and logic for modeling physical phenomena. There are quite a few physicists and mathematicians who don’t believe math is an intrinsic part of the universe.
It’s not at all clear that the Law of the Excluded Middle is an intrinsic part of the universe.