Hi @AR,
Thanks for reaching out to Q&A.
CORS and IP whitelisting are both different concepts. It all depends on the 3rd party website.
If a specific resource in the website or the website itself blocks cross-origin requests, then you will have to add the function app url ("appname.azurewebsites.net") to the 3rd party CORS list so that the function can access the 3rd party website. This would work even with Consumption SKU.
On the other hand, if the 3rd party website has IP restriction enabled, then you will have to whitelist the outbound IP address of the function app. If you would like to have a dedicated IP address that doesn't change, then you have to make use of NAT gateway as you mentioned.
Hope this helps! Feel free to reach out to me if you have any queries or concerns.
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