Miners may refuse to include a transaction in a block if it comes from a flagged address. But this is almost never the case, as the vast majority of pools only make selections based on the level of fees paid for transactions.
A few months ago, it was discussed whether miners and pools might one day be pressured to refuse transactions from certain services, such as mixers for example. For the moment, this is not the case. I know that one pool has already refused to include tx in blocks under the pretext of AML compliance, but I don't think that's the case yet.

If you're talking about double-spending, this could be a problem if merchants deliver the product/service before a transaction is confirmed in a block. Once the transaction has been confirmed and included in a block, it becomes irreversible and double-spending an unimaginable thing.

Otherwise, OP, I can recommend reading Mastering Bitcoin, which is an excellent and free book about Bitcoin's technical and functional aspects.  Likewise, if you haven't read it, I suggest you read the Bitcoin White Paper written by satoshi, it's available in most languages and should answer your questions objectively.