I‘ve actually done something similar. You could add the Webflow CMS-Item ID to memberstack profiles and the CMS-Item in Webflow. Then add it in a hidden textfield in your page. Afterwards I use a little Jquery to remove all items that don‘t contain the ID.
I did this recently using Chris Spags’ Jetboost.io filters by adding a hidden form on the page that has a custom input attribute of name: “data-ms-member” and value: “membership-ID” (you could use emails or any other field)
You can then create a CMS with a multi-reference field to user’s emails that Jetboost filters on. So as soon as the page fully loads, it then filters the CMS to only show the matching items.
It’s not perfect - sometimes a slow loading page will show all CMS items until the filter kicks in, but it works for me for now using non-sensitive information.