There is a 'Tapestry test' game in alpha.
My hypothesis would be that the configuration of all tables of each player can't be changed. That mean if the last table created for a player on that game was in training mode, then the next game would be in training mode.
Furthermore you can only play solo game in training mode. Which explain why some players can join and some can't.
I've got a similar bug when I was trying to join an alpha game without being a reviewer in the 'see all available games' in the loby. Couldn't see the game but could join it.
@BoooardMaster, can you try to rematch this game instead, then goes to the lobby, and start your game from the lobby without entering your game:
https://boardgamearena.com/table?table=295606114