I didn't get a reply yet, so I investigated further. It appears that the project isn't actually opening as modified, but if I open another project in front of it without closing it, it becomes modified when I click "Don't close" when opening the next project. It's the only project among the group of about 11 that I frequently keep open simultaneously that becomes modified by opening another in front of it, however. In case you're wondering, I have an automation macro that opens all 11 projects that way, but the situation doesn't seem to depend on whether I use the macro. This must be related to the Logic Pro X's partial support for having multiple projects open at once. I refer to it as "partial support" because it's not possible to select multiple projects in an Open dialog, nor is it possible to open multiple projects by selecting all of them in a Finder window then double-clicking one, or choosing Open from the File menu. AFAIK, it's also not possible to disable the prompt to leave the current project open when opening another.
Another question might be why I open so many Projects at once. The only other way I know of to open a playlist so that each item to be played must be started manually rather than starting automatically is to use MainStage, and I've had enough unexpected events occur with every version of MainStage I've tried (including the latest), that I'm reluctant to use it for that.