Hi @Adam Westwood ,
Thanks for reaching out to Microsoft Q&A.
If your Azure Web App's IP got blacklisted by SURBL because of shared IP usage with sketchy tenants, don't worry, you can fix it. First, try getting a dedicated outbound IP by hooking up your App Service with a Virtual Network (VNet) and setting up a NAT Gateway. This way, all outbound traffic goes through a static public IP, cutting down the risk of blacklisting due to other tenants. Check out Microsoft's guide on setting up a static outbound IP here: Azure App Service - Inbound and Outbound IPs. Also, locking down your app with IP access restrictions helps keep unauthorized access at bay. More info on that here: Azure App Service - IP Restrictions.
Once you have a dedicated IP, ask SURBL to remove your new IP from their blacklist. Just provide the necessary details, like your dedicated IP and proof that your app isn't doing anything shady. Make sure all your security measures are solid to avoid future issues. You can also check this guide for how a domain was successfully removed from the SURBL blacklist.
These steps will help keep your app safe and ensure your emails get through.
If the answer is helpful, please click Accept Answer and kindly upvote it so that other people who faces similar issue may get benefitted from it.
Let me know if you need more help.