If we assume a perfect world where every single element is shaped/cut/fit/installed exactly perfectly, a tiltback should be more stable than a straight headstock, for heavy vibrato use. If you've ever tried an early Gibson or Epiphone archtop (or a modern Gibson Custom Shop recreation) with a Bigsby then you know that you can get about two steps of dip and a half step of rise out of one, all night long, without neutral tuning shifting in the slightest.
But in a world of mass production parts where everything is picked up off the CNC, dusted down and shipped, you can't expect that kind of consistency any more, and the simpler you can make a guitar now the more likely it'll work. For mass production parts—including Warmoth's—a straight headstock is definitely the safest option.
I will say that the most stable option with modern parts and tolerances is to split the difference and have either a very slight tilt or staggered tuners on a straight headstock, so you get just a little bit of downward pressure over the nut but not much. Better than using a retainer bar/T/tree, which will nearly always just snag the strings. If you check out Brian May and Jeff Beck, both their guitars use a very gentle break angle at the nut (May has a tiny angle to his headstock, Beck has staggered tuners) and nuts that barely hold the strings at all ('0' fret with bottomless nut for May, Wilkinson roller nut for Beck) and they can abuse their vibratos heavily without issue, as can you if you pick up one of their signature guitar recreations.
Also bear in mind that the sideways angle the strings come through the nut also matters. 3x3 headstocks, even if they're 'straight', often require the strings to bend slightly left or right when exiting the nut to get to the tuner. Getting the tuners completely in-line with the nut slots greatly helps tuning stability with a vibrato. (Another stumbling block for many mass production parts.)
