Would I be violating Twitter's policies if automated a process whereby, when I compose a Tweet, the words I write (which are my own) appear simultaneously on something other than Twitter? Is it the round-tripping through their API that has Twitter's undies in a bundle? Because I could just skip that part entirely.
You should just skip it regardless. It's fairly obvious that Twitter has become a bad actor and should be removed from the content and communication pipeline.
AT&T used to dictate which phones you could connect to their network, too, and that was also a terrible idea.
Best way of putting it that I've seen. These recent moves serve to alienate developers (and users by extension) and reek of typical corporate desperation.
I seem to recall they now have a policy specifically forbidding Twitter client applications from simultaneously posting to other services, so you probably would be violating their new rules.
p.s. I don't use IFTTT but this is my guess.