I've tried to reproduce this (in Word for Microsoft 365 on Windows 10) but the tab key does move the cursor from one plain text content control to the next, including from one repeating section to the next.
The only time I see the tab key inserting a tab character is when I press the tab key in the last plain text control in the last repeating section. Then the cursor goes to the beginning of the first repeating section, to the left of the first plain text control, and inserts a tab there. If this is your problem, then there is a macro solution using the ContentControlOnExit event handler. See https://learn.microsoft.com/en-us/previous-versions/office/developer/office-xp/aa140279(v=office.10) if you need that.
Otherwise, I suspect there's more in your document than you've described. It will probably be necessary for you to post a sample document on OneDrive or another cloud storage site and post a sharing link to it here, so we can examine the problem and determine its cause.