How can I make this plugin work with a membership plugin that is role-based?

Hi,

Our plugin is only compatible with the WooCommerce Memberships plugin.

From the plugin’s description here are a few relevant points for your situation.

“…grant access to a membership as part of a product purchase…”

“…Plan Content Restriction
This gives you more control over how members begin using your site and lets you introduce members to your content at your pace…”

So it looks like it might meet your requirements.