If you have a central authority which is keeping track of the ledger, they always have the ability to disallow any given transaction at their discretion or at the behest of some more powerful organization, e.g governments

This is one of the problems that crypto was attempting to solve (if implemented properly and used correctly). There is a third party(the "network"), but its decentralized and at least for "proper" networks, no one organization has a controlling interest in the network

Now any given miner/producer does not necessarily have to accept any random transaction. In practice however, for mature networks such as Bitcoin there are so many different miners/producers, its unlikely they would all conspire to disallow certain accounts or types of transactions.

Now this is certainly possible for a crypto exchanges and therein lies the rub with cryptos - if you want to get the cryptocoin, you generally have to buy it with good old fashioned hard currency. Conversely if you want to convert the cryptocoin back into hard currency. And exchanges nowadays are facing increasing regulations from governments. Which means practically you are still largely under the thumb of those powerful organizations without some real gymnastics involved, such as trading crypto for cash with a real person in a back alley somewhere, or vice versa