Hi @IsaacS 
welcome to the forum.
What you’re asking for is doable, but there is no simple answer that solves it. It’s a bit of a “build” to make it happen.
That said, here’s a walk through for you…
You mentioned wanting to use Webflow Memberships.
You can gate access to a CMS Collection with Memberships so this part is straight forward. Only allow logged in members to view this collection.
The act of registering could be a (multi)reference field on the events collection. It’ll reference those users who have registered.
This is accomplished by having a form button that submits to Make (Integromat) or Webflow Logic and adds that to your cms.
Now that event cms collection page can display those references (users who are coming).
The Problem
The problem that unravels is your memberships and your cms are two separate “things” that have no association to one another.
You’ll notice in your Webflow Designer that they are literally two separate items:
…and Webflow has yet to natively provide a way of linking them together.
The trick is you’ll need to manually associate a member to a cms collection.
There are a few ways to do this but the simplest is to use a Webhook that notifies you when a new member is created.
Once notified, you can then populate a cms collection with this information.
Now you’ll have everything you need within your cms and you can use those associations mentioned above.
Here’s a forum post from a few days ago where I walk through how to create Webflow Webhooks that trigger when new Members are created or updated.
That walks through using Zapier, scroll down and I walk through using Make (Integromat) to setup Webflow Webhooks. You could easily swap those out for Webflow Logic by using the “incoming webhooks” trigger instead:
Those are the basics of getting this build wired together and working. There are a few nuanced stumbling’s along the way, but nothing that prevents you from making this happen with Webflow Memberships.
Hope that helps!