random bills & deposits are greyed out
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I do not believe those grayed out Reminders appear randomly: I believe those grayed out Reminders appear because they are not the most current un-entered Reminder for that payee (so they can not be Entered now from the displayed Reminder - as also strongly suggested by the fact that those future Reminders do not display an "Enter" button).
The Monthly Bills & Deposits tab only shows Reminders for a single month at a time. That makes it impossible to see Reminders for previous months - grayed Reminders tell the user that there are, indeed, Reminders with earlier Next Due dates that have not yet been Entered.
Entering all earlier Reminders for the same payee will un-gray those grayed out Reminders.