Of course anything could still happen, but...
My hunch is that we will be able to unofficially run the Catalina GMs on our vintage graters. I don't think Apple is really interested in being punitive to its cMP stalwarts (which, implementing an AVX-requirement during the beta cycle would most definitely be).
As I said before Catalina/MP7,1 was even announced I believe Apple was on track to allow Catalina on the 5,1. Their track record with macOS going back 6+ releases now is that they only drop compatibility every other year. It's a revolution->evolution cycle. And Catalina is definitely an evolution from Mojave. This has been borne out by the fact that the MacPro5,1 is the only model dropped for Catalina.
I'm not sure when Apple first got word of the new MDS vulnerabilities (early this year?), nor when Intel made its decision to leave the ≤ Westmere CPUs unpatched, but I think Apple would say their hands were forced by that situation. By granting another year of OS support they would be extending the amount of time vulnerable cMPs were officially supported and basically giving their approval for customers to keep using them.
Also, consider how "difficult" it is to flash firmware on the cMP. We in the enthusiast community tend to forget that a sizeable number of cMPs currently in use haven't even received one firmware update simply because installing one is a manual process (and a convoluted one at that). Never mind that the "fix" of disabling HT appreciably diminishes performance for many tasks, are we even 100% sure at this stage that disabling HT fully mitigates the entire array of vulnerabilities recently disclosed? I remember tsialex saying something about AES-NI being a separate factor. Maybe that ended up not being exploitable on its own (I barely understand the technical aspects of these flaws), but I do see where Apple is coming from here. Not everyone using a MacPro5,1 knows how to protect themselves from these flaws.
That said, I really don't see Apple forcing everyone off the platform--especially with some of the tough press they've gotten about the cost of the 7,1. Just like with the 4,1>5,1 cross-flash, they'll most likely put their usual blocks into place, knowing that will be enough to keep away casual users, while continuing to tolerate power users taking matters into their own hands (with the tacit understanding that support from Apple is nill).