To defend Wildberger a bit (because I am an ultrafinitist) I'd like to state first that Wildberger has poor personal PR ability.
Now, as programmers here, you are all natural ultrafinitists as you work with finite quantities (computer systems) and use numerical methods to accurately approximate real numbers.
An ultrafinitist says that that's really all there is to it. The extra axiomatic fluff about infinities existing are logically unnecessary to do all the heavy lifting of the math that we are familiar with. Wildberger's point (and the point of all ultrafinitist claims) is that it's an intellectual and pedagogical disservice to teach and speak of, e.g. Real Numbers, as if they're actually involving infinite quantities that you can never fully specify. We are always going to have to confront the numerical methods part, so it's better to make teaching about numbers methodologically aligned with how we actually measure and use them.
I have personally been working on building various finite equivalents to familiar math. I recommend anyone to read Radically Elementary Probability Theory by Nelson to get a better sense of how to do finite math, at least at the theoretical level. Once again, on a practical level to do with directly computing quantities, we've only ever done finite math.