> Is there an alternative service one could use? Is there a way not to give these shady companies power to steal all my money?

There are many alternative services listed in other comments, but to be clear, every single one of them has the power to do exactly what Stripe did.

There is no way to accept credit card payments without accepting that power to freeze suspicious incoming payments, simply because fundamentally credit card payments are not final and can (and often will) be reversed afterward, and if someone promised to never freeze merchants' funds, every fraudster in the world would come to try out their services, bankrupting them in the process.