This is a bit of an older technique, as since Maniaplanet 4.1 this patch is not that important anymore. Many titlepacks have worked around this issue by implementing custom Maniascripts and adding custom vehicle items to maps. If for some reason you want to natively play with non-Stadium cars in Stadium though - here's a description.
With the Stadium Unlock plugin, it becomes possible to unlock the Stadium environment mixing in ManiaPlanet. This is normally intentionally blocked by Nadeo for several reasons, but technically everything works just fine.
The following titlepacks have been selected to automatically enable this patch:
Please contact Miss on Discord or do a pull request on Github to add your own titlepacks to this list.
To make maps in Stadium with a different car, open a multi-environment title pack (such as TMAll@domino54), and create a new map like normal and select any other vehicle.
Note that when you save and load such maps, you might need to enable the Stadium Unlock patch in order to play these maps again! If the patch is not enabled, you will spawn in with the regular Stadium car.
For titlepacks not listed above, you will need to enable the patch manually. To do so, go to Scripts -> Stadium Unlock, and make sure it's checked.