Symptoms

On Service Portal, when the snc_external user clicking on "Add" button of the multi row variable set, the screen gets greyed out instead of opening a popup window to add variable values.
Below screenshots illustrates this issue behavior,

Release

When the user clicks on "Add" button on the multirow variable set, following OOB "Table Variable Active Row" widget is returned by the "api/now/sp/widget/widget-modal" REST API call. Then eventually rendered to the user.
On the affected instance for the "snc_external" user, "api/now/sp/widget/widget-modal" REST API call not returns "Table Variable Active Row" widget, due to the reason that "Service Portal User Criteria Support" (com.glide.service-portal.user-criteria) plugin is activated instance and "glide.service_portal.user_criteria_enabled" property is set to true.
With this configuration, the system will honor the user criteria over the roles defined on the widget. However, "Can view" user criteria is not set on "Table Variable Active Row" widget.
Thus, not showing the modal window for the snc_external user with the onlick of "Add" button of the multi row variable set.

To resolve the issue, perform one of the following workarounds,

On the "Table Variable Active Row" widget, with the "Can view" related list add "SNC External" user criteria, OR
Set "glide.service_portal.user_criteria_enabled" property to false, you can also set this property via UI as per the following Set the user criteria for Service Portal system property

Above mentioned KB article KB0745527 describes the same reported issue, however, the root cause discussed in this article KB0752941 differs from it.