You can certainly run charges outside of MyVR using something other than a Stripe account. However, please note there would be no automatic recording and tracking of those charges within MyVR, so you would need to record them. Additionally, we cannot offer support for any charges created outside the MyVR system, as we won't see them!
We currently work with only Stripe to connect merchant accounts to MyVR. In order to use MyVR to collect payments from your renters, you will need to set up a merchant account with Stripe.
Fortunately, Stripe makes it incredibly easy to set up a merchant account - typically you are up and running in under 5 minutes.
You can learn more about Stripe at stripe.com.