The promise that a miner somewhere in the world will validate your transaction if you pay a large enough fee is one of the main features of Bitcoin. Put otherwise, Bitcoin resists censorship. When this subject is discussed, the term "censorship resistant" is used instead of "censorship proof" for a very good reason. A single miner has complete control over what they censor; that is, they are free to exclude anything from any block they mine. But when other miners detect a transaction, they cannot stop them from putting it in their own blocks.

Although it resists censorship, Bitcoin is not impervious to it. Without considering the potential opportunity cost of income loss in the event that there are insufficient transactions available paying a feerate comparable to the transaction(s) they want to censor, any miner is free to censor anything they so desire. However, unless such miners: 1) make up the majority of the network hashrate; or 2) decide to use that reality to orphan the block of any other miner who decides to process the transaction or transactions they intend to censor, the global system will still execute that transaction.

As long as a minority of miners continued to mine blocks that contained the "verboten" transaction, doing so would result in the loss of money for the majority of miners involved in the orphaning attack. The majority of censored miners' average income would decrease because each time a block of that type was discovered, it would effectively lengthen the period before the next block that made it into the chain was discovered. This would continue until the minority (who would be losing out on revenue from any block, including the censored transaction) gave up and submitted or went out of business.

Let's suppose for the time being that this situation is unlikely to occur. If that were the case, Bitcoin would either be doomed to remain in this form or would need to continue operating until non-censoring miners gather enough hashrate to subdue the current majority's desire to leave transactions in blocks that they do not want verified on the blockchain.

What occurs then, if a minority of miners opt to filter a particular subset of transactions from their blocks? The blockspace that those transactions can use gets smaller. Compared to all other transaction classes, they have fewer accessible blocks. What is this going to wind up doing? Compared to other transaction classes, this one will experience saturation of fees more quickly.