Yes, I think that Stripe is a secure payment option if it is implemented probably (which is the case for any payment option) If it is poorly implemented then it is open to all sorts of venerabilities but if is properly implemented then there is no reason it isn't a secure payment option
A major corporation such as Apple would not partner with Stripe if it felt that it was not a secure payment option for its customers. The liability issue alone would ensure that Apple extensively tested the security of Stripe. It's simple to say that if you trust Apple with its own security, you'd be safe with Stripe.
In today's time, nothing is completely secure, especially in terms of technology and cloud based options. Apple's new pay system in which they have partnered with Stripe may have advanced security measures that past options have not included, but with time it too will be hacked just as all previous payment systems.
Stripe is not secure. This is because no online payment system is entirely secure, especially not a new service. Companies all make mistakes when they are young or new, and I would not place my trust in a new service so quickly. They have to be able to prove themselves.