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I am not a tech expert so would any of those 2 options fix the problem?

Allow only avatars from third party websites such as imgur?

Or

Allow only avatar uploads from your webserver(so people just upload it ur own server)?

Or none of them would work ?

The second one would fix the problem. The problem is caused by the first feature.

Note that this isn't an exploit, it's how the Internet works. Your public IP will always be public.