I started using privacy.com for this reason. You can spin up a separate card number for each transaction type with its own limit (e.g. $100/month or $200). You can also just turn them off at will.
There are other services, though not as advanced. In Europe you could use Revolut to create virtual disposable cards. They are more useful for one-time payments however.
privacy.com looks great. I think the only disadvantage is that you lose all the 2-5% cashback, travel benefits and so on. I wish they could produce card while keeping these benefits but still its good card to have for shady websites.
I use privacy.com and my regular card. I use my privacy.com cards for sites where I think security is bad (like our local water company) and for recurring subscriptions on sites that I don't think will be easy to cancel.
It's a good compromise between protection and credit rewards.
Credit card companies and banks receive 1-3% of commission on all of the transactions made throught he card. Banks normally pass parts of these along to the consumer in the form of cashback or other benefits. Privacy.com just uses these commisions as funding for their service. (I've read it somewhere on their site)