Hello,
Please always make the full site backup before update.
As for Wishlist, Starting from Basel 5.0 we have integrated a Wishlist functionality into the theme. It means that there is no need to use YITH Wishlist plugin. The Wishlist feature is enabled by switching it on in the Theme Settings – > Shop -> Wishlist https://xtemos.com/docs/basel/basel-wishlist/
Please read these suggestions as well https://xtemos.com/docs/basel/faq-guides-2/4-x-5-0-migration-guide/
If you still have the problem with saving the changes, deactivate all the plugins not related to the theme and check the issue, if the problem remains, leave the plugins not activated and provide the site admin access to the private area
Best Regards