A server 'processing' (which seems to include using it in any way, not just storing [1]) your IP address appears to fall under the GDPR[1], and said server would be in violation of the law unless its processing falls under one of the exemptions.
The main exemption appears to be getting the user's explicit consent, though there's also this super vague exemption: "for your organisation’s legitimate interests, but only after having checked that the fundamental rights and freedoms of the person whose data you’re processing aren’t seriously impacted." [2]
In general, it seems very hard to avoid the GDPR because what is considered 'personal data' is extremely broad.
Maybe I'm misunderstanding something.
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[1] https://ec.europa.eu/info/law/law-topic/data-protection/refo...
[2] https://ec.europa.eu/info/law/law-topic/data-protection/refo...