It might be the case that the plugin author limits plugin access to OpenAI IpAddress only.
You probably need to check how Authentication is implemented for plugins.
Also, check the following post for your reference:
I am not sure but there might be some clamor for plugins to be used outside of ChatGPT and this might eventually make the plugin authors to authorize other sites to use their plugins. It could be a potential revenue stream for them since, as I understand, they are not allowed to monetize their plugins in ChatGPT. So if they can also provide ways for other ChatGPT clones or chatbots to use their plugin, it can be positive perhaps.