Eh? Can't miners refuse to include transactions that don't adhere to new conditions in addition to old ones?

If 51% of miners decide to, after block #N, not include any transaction that doesn't satisfy the predicate P in any block they produce, nor mine on any chain which has a block after block #N which has a transaction that doesn't satisfy predicate P, then the longest chain will have all the transactions after block #N be ones which satisfy P, and furthermore, if the other 49% of miners are aware that this is happening, if they want their blocks to be in the longest chain, they have incentive to follow the same rules when mining.

This is the logic behind soft forks, is it not?

No, you're misunderstanding everything. The consensus mechanism is about agreeing about the contents of the blockchain, not about the rules that make up the bitcoin protocol.