Nope, the mechanism is not assessing what code is in the url being called in the task, if that's what you mean by "the script" doing that writelog. 🙂
So when you say you "had never checked the Publish checkbox", the simple question now is whether that BOX IS checked as you view the task. If it is, and you don't care to have the task's output saved, then just uncheck it and you're done.
(To be clear, the update would NOT have somehow caused cf to now make the task now publish its output. Indeed, the 3rd issue above new to the May update literally REMOVES any tasks that publish output, if not whitelisted in that pathfilter.json file first.)
Let us know how it goes.
While we await your news of trying what I proposed (which is far simpler than what BKBK proposed after that), I'll add that I've since confirmed that it was in fact CF11 which implemented the change that required if any scheduled task was set to "publish" or "save output to a file", the extension must end with txt or log.
I bring this up first to say that your issue really can't seem to be related to your having done the CF update. (I realize you said that you didn't think you'd clicked that "publish" option for your task. Again, uncheck it in that case and proceed with your desuired update.)
But second, in case any future readers may find this and wonder how to control that set of choices of log,txt (as shown in the CF admin error mesage you quoted), that actually CAN be controlled via a setting in the neo-cron.xml (such as in CF's cfusion/lib, or [instancename]/lib for those running more than one), where one will find a setting:
And this, too, was documented when CF11 made the change. One would need to restart CF for that to take effect.
Finally, since all this came up, it got me wondering why there's no CF Admin setting that controls tat set of values. It could EASILY be an input field on the front page for scheduled tasks (where some other global scheduled task settings are set). I made a feature request to that effect today at https://tracker.adobe.com/#/view/CF-4227162.
Sorry this second point about the setting is getting away from your simpler problem. Hopefully you can just uncheck the publish setting for your task, get your task update done, and enjoy the the weekend. 🙂