But I wonder what's more likely, that looking at everything through red-tinted glasses makes everything look red, or that "mathematical entity" somehow isn't oxymoronic.

Lee Smolin, for instance, criticizes many theoretical physicists for mistaking their mathematical map for the territory. The alternative is to resort to metaphysical idealism in equating the nature of our tools with the furthest nature of reality. What could it even mean to say that a structure is purely mathematical or formal?