Yes, if you prefer 24Hz output, just set the Strato to “Allow Display Mode Changes”, and it will switch to 24p output for film content.
The reason that the Strato defaults to 60p output is that the Kaleidescape onscreen display always runs at 60 frames per second for smooth animation, and some displays take a few seconds to re-synchronize when the source switches video format or frame rate.
As mentioned by Mr. Poindexter, many displays include a feature called inverse-telecine (often referred to by some brand-specific name). Telecine is the process by which film content’s 24-frame-per-second cadence is converted for display on television screens, so inverse-telecine un-does that conversion. As you noted, telecine can introduce some amount of judder. Typically it’s not a huge amount — many people don’t notice at all. This was necessary when displays had 60Hz refresh rates.
These days, it’s common for displays to have 120 or 240Hz refresh, and 24 obviously divides evenly into both of those numbers. So, to eliminate any judder, the display may employ inverse-telecine to recover the original 24p source, so that they can simply map that 24Hz signal onto their native 120 or 240Hz panels.
As an example, let’s say a projector has a native refresh rate for its panels of 120 frames per second. If Strato is outputting 24p content converted to 60p, the projector’s inverse-telecine will internally re-convert to 24p, then simply display each of those frames through five panel refreshes, so you get no added judder. (This assumes that you’ve turned off motion-smoothing, which would otherwise add interpolated frames rather than simply repeating frames.)
You can play with this to see what looks good to you. On my previous projector, I found the inverse-telecine to be near-perfect, but every now and then it would have a little hiccup, and those were distracting enough that I set up my players for “Allow Display Mode Changes” and accepted a few extra seconds of black when I started a film.
My new projector’s inverse-telecine is rock solid, so I switched my players to Minimize Display Mode Changes because there’s no visible difference to me compared to running the player at 24p, and I get slightly faster startup times.
Sorry for the long-winded answer. Occupational hazard.