In what sense does the "speed limit" $c$ prevent violations of causality? Could they be prevented some other way? I have seen it said that if we want to avoid violations of causality (I can see why we would want to avoid that!), we need the information-transfer "speed limit" of c.
I presume(?) this assumes some other stuff in the model though? Consider a 2D universe of discs moving uniformly and bouncing off each other elastically. It's not obvious to me that those violations of causality are possible in this universe, and I have not defined squared interval or anything like that.
Is it only when you bring in GR or electromagnetism that you need extra stuff to maintain causality? Is there any generality to this use of the word "causality"?
Optional philosophical part:
I am a fan of Quantum Computing researcher Scott Aaronson, who has a convention-defying spiel in his book and course. I'm going to paraphrase him / say how I see his thinking:

quantum mechanics is totally natural and inevitable and one of the best things you could possibly base a universe on. Ok, so we had it forced upon us by experiment, so it's not like we have a choice in whether or not to view the world as being based on QM. However, even if it wasn't, QM would still be extremely interesting and sensible, because if you mathematically describe certain things you might want the world to have (algebraic closure for example), you'll find QM drops right out of them. And in particular, all the folks telling you it comes out of nowhere and is just unpleasant and convoluted crap coming from experiments that you just have to deal with - they are wrong.

More generally than this thing about causality, what Scott Aaronson wants/says he has for QM, I would like for SR/speed of light/relativistic product.
One could well disagree with Aaronson about the above! It would be polite to read his book first. But even in all of that, he admits he is still not completely sure about some parts (eg https://www.scottaaronson.com/blog/?p=4021). But maybe, for SR, we DO have this "drops out of reasonable mathematically-stated requirements for a universe design"?
 A: Having c as a speed limit is not sufficient to make causality hold. In general relativity, you can have things like naked singularities and closed, timelike curves that violate causality.
It's not really even true that Newtonian mechanics has causality:
https://en.wikipedia.org/wiki/Norton%27s_dome
In special relativity, causality isn't the only thing enforcing c as a speed limit. Particles have a conserved mass, and because $m^2=E^2-p^2$, massive particles are restricted to $E>p$, which implies $v<c$. For similar reasons, massless particles travel at c (and tachyons >c). The geometry of spacetime also prevents FTL frames of reference from existing, and disallows any continuous process of acceleration through c; this holds regardless of whether matter even exists.

Consider a 2D universe of discs moving uniformly and bouncing off each other elastically. It's not obvious to me that that violations of causality are possible in this universe, and I have not defined squared interval or anything like that.

This does not violate causality in Newtonian spacetime, or in SR if wave disturbances in the discs propagate at less than c.
You may want to look at energy conditions: https://en.wikipedia.org/wiki/Energy_condition Your discs will violate energy conditions if they are perfectly rigid or if the speed of sound in them is >c.
