The current rule is you don't need to show the mod list or press esc unless the run is seeded.

Of course, the status about Mods Enabled appears on the final screen, but the problem here is that if you start a new game with mods on, turn off mods, and then restart to the game, the final screen will not show the status for Mods Enabled.

By exploiting this, you can fake it as a random run by loading a seed you want, then disabling the mod and restarting the game.

If you press ESC even once, you'll still see a small message at the bottom of the screen saying 'Mods used', but there's no guidance on this in the current ruleset, so the potential for abuse exists.

Is there a way to check if a mod is enabled on a random seed without pressing esc other than the way I know? If not, are moderators willing to change the rules a bit?

This is a good point. I will add an amendment to the rules that you must hit "ESC" at least once during the run, so that way we can verify no unlisted mods have been used.