After a day of pulling out my hair, I found out that the problem is with the new ‘Default Customer Address’ option in WooCommerce. If you select Geolocate Woocommerce appends a string to all urls ?v=XXXXXXXXXXXX. For some reason this breaks the password reset sections. Once disabled my customers are able to reset their passwords and enter a new password once the URL in the email is clicked.
I’ll mark it as resolved, but I think this is a bug in WordPress and / or Woocommerce