Plenty of Trump's EOs have been ruled unconstitutional. He may feel that his authority extends beyond checks and balances, but it doesn't. His attempts to abuse his power have been duly mitigated and stopped about as well (or badly depending on how you look at it) as the last few presidents, as I see it.
Because a computer program is an expression, and the right to free expression is a cornerstone of the first amendment. So broadly, I don't think the government can "ban" an app, no matter who wrote it.
This proposition has been tested and affirmed for source code (see DeCSS t-shirt, etc.) but to my knowledge has not been tested for binaries. So, it would at minimum be a new test of whether binary code is as much a protected expression as human-readable code.