I am the exact same way, I use privacy cards for almost everything online. However, I have used RallyFuel a few times now and it has been totally fine. They use standard secure payment processing, so they don't actually store your raw card data on their servers. It is as safe as buying something on Amazon. You can verify the security yourself if you visit
https://rallyfuel.com/athletes/taina-mair and look at their payment gateway info. It is legit, so you don't need to worry about identity theft there.