I'm not basing my judgement on the pedigree, I'm basing it on the content. What constructor theory is about is assigning and re-assigning concepts and language to existing physical theories. That's called "metaphysics," a practice that believe it or not predates physics. (Philosophers have been formally assigning concepts and language to informal physical theories long before the first formal physical theory was articulated.) It's not like Deutsch is in bad company, Aristotle also wrote about metaphysics.
Nonetheless, that does nothing to change the fact that crank websites almost always share three elements: they are works of metaphysics but claim to be physics, they have way more popular writing than academic writing (in this case, see the size of the media page vs the empty publications page), and they have a website advertising them (that's actually pretty unique to cranks, for some reason). I don't really have an axe to grind, it's just that the linked page is a typical crank website.