I'm just thinking on whether "free, secular" or "compulsory education" are the bigger contradictions, I could not possibly write something like this unless my own thinking and knowledge were very, very limited AND limiting.
I'm in favor of a laicistic rather than a secular society. The point is, the public space should not be limited to one creed but be open to everyone including those without religion and no faith should be pushed on people against their will.
As for education, I think a tuition free, compulsory and religion-neutral education is necessary for a person to be able to fully develop, blossom and enjoy intellectual, social and psychological freedom. It's also why I am strongly against homeschooling which unnecessarily limits a child's access to the world and exposes it to extreme filters.
Now for the actual question:
As opposed to material riches? Are spiritual riches different to culture or tradition or norms?
To me, spiritual riches are things like an appreciation for art, human connections, nature, beauty, awe at the cosmos and the world around us. It is sensing something far greater than yourself and feeling grateful for it rather than treat or intimidation.
Culture and tradition are immaterial (as in "not material") values, for sure, but I wouldn't consider them spiritual riches by the above definition. However, somebody who deeply enjoys and appreciates their culture and traditions could be considered to be spiritually rich.