Hello,
That’s very strange because I don’t see the mentioned button if the Storefront theme is enabled https://gyazo.com/b77d2acd2363c0c5744e98bc5bf97578 So, it looks that you have some glitch with this. Contact WooCommerce support https://wordpress.org/support/plugin/woocommerce-gateway-stripe/ to make the button always work with the Storefront theme first and then reply back if you still have issues with our theme after that.
Because as this moment it works only in test mode.
Regards