I'm using Lightroom (cloud version). I am renaming the pictures to include a sequence number but that apparently doesn't change anything since the pictures are already in a strange order before I do that. Same thing for the app I'm using to visualize the exported pictures... it doesn't matter since the reordering of the files happens within Lightroom when I go from the edit module to the export module. Thanks again for your help.
OK, I've done some further testing and I think you've come across a bug in Lightroom, which I'll report.
There are basically 4 ways to implement the Export process in Lightroom: Using File menu>Export, Using keyboard shortcut Ctrl/Cmd+Shift+E, using the Share Icon at the top right of the window, or using the right-click>Export option. The first 3 work correctly, but the last one does indeed seem to mix-up the images in the Filmstrip into a random order.
So try one of the other options to initiate the export to see if that works for you.