Alex here, from the Shopify support team.
We should definitely be able to get that figured out. Each theme has a section where you can make edits to the language of your storefront. This can be found by going to Online Store > Themes > More Actions > Edit Languages. It will look like this:
Once you've pulled up the language editor, type the language you'd like to change into the filter section:
Then, find the matching text for the section you'd like to change, and update it to "Members Only".
I hope this helps! The language editor is one of the most underrated tools for Shopify themes, in my opinion. There's a bit more on how it works here if you're interested. Feel free to follow up here with any other questions. I'll keep an eye out!
Alex | Support
|58 seconds ago|