No it isn’t at all.

GDPR allows you to store data about people provided it’s necessary to provide the service or meet legal requirements.

GDPR prevents you from storing more data than it needed and from storing data longer than you need it.

GDPR requires you to inform users what data you are storing about them, when requested, and to delete any data you hold on users when requested.

Since this would be a legal requirement there would be zero conflict.