As software developers, the essence of our profession is to automate repetitive tasks. If you have a rigorous manual testing methodology for your software, it should be a trivial task to turn that test specification into automated tests. The absence of a suite of automated tests is a major red flag in any non-trivial software project - it strongly suggests that either the developers do not care about quality, that they do not understand their work well enough to manage quality in a systematic way, or that they are too haphazard and disorganised to manage their project appropriately.
But cults do not do that, they just accuse non-believers, in this case, that they do not care about correctness.
That's like saying Messner and Habeler did not care about safety because they climbed extreme pitches unroped where other pairs roped up and moved one at a time. But M&H were very good climbers and got up and down twice as fast as the others, who doubled their risk of the weather turning on them by being "safe". If you know your mountaineering, the latter is usually how folks die on mountains.
Did you ask them about their practice? Did you ask how often they had to roll back deployments, or at least take a hit on something automated testing would have caught?
I asked them about their testing - turns out they were looking to have someone help them develop a way to test their software (so at least they want to do it).
I wish I'd asked them the two questions you listed at the end, they are much better questions than a bland "do you test?". They did break the build some times.
btw, I am glad no one asked the alternative to testing -- it would have been more a textbook on software development. <g>