The default mempool policies in Bitcoin Core are effective at preventing OP_RETURN outputs with more than 80 bytes of data. They are NOT effective at preventing OP_FALSE OP_IF ... OP_ENDIF (inscriptions) and fake public keys.

Transactions have been shown to somewhat reliably propagate to all nodes that accept them if at least 10% of the node population accept them to their mempool. Even a strong majority of the nodes of up to 90% of all nodes would have little to no impact on the propagation of consensus valid non-standard transactions relayed by the other 10% of the nodes..

Additionally, Libre Relay nodes, an implementation with less strict mempool policy than Bitcoin Core, preferentially peer with other Libre Relay nodes which means that they effectively relay transactions among each other even with much smaller network penetration, and some mining-pools accept direct submissions through web interfactes or APIs that do not rely at all on network propagation.