GDPR Article 4 paragraph 1 says:
‘personal data’ means any information relating to an identified or identifiable natural person (‘data subject’); an identifiable natural person is one who can be identified, directly or indirectly, in particular by reference to an identifier such as a name, an identification number, location data, an online identifier or to one or more factors specific to the physical, physiological, genetic, mental, economic, cultural or social identity of that natural person;
Recital 26 says
Personal data which have undergone pseudonymisation, which could be attributed to a natural person by the use of additional information should be considered to be information on an identifiable natural person. ... The principles of data protection should therefore not apply to anonymous information, namely information which does not relate to an identified or identifiable natural person or to personal data rendered anonymous in such a manner that the data subject is not or no longer identifiable.
Recital 30 says:
Natural persons may be associated with online identifiers provided by their devices, applications, tools and protocols, such as internet protocol addresses, cookie identifiers or other identifiers such as radio frequency identification tags. This may leave traces which, in particular when combined with unique identifiers and other information received by the servers, may be used to create profiles of the natural persons and identify them.
An IP address hashed through a cryptographically secure one-way hash cannot reasonably be used to establish the original IP address, nor to geolocate, nor to directly identify the data subject. However if such addresses are stored in a database with a link to the subject's individual record, or to other data which identify the data subject, then they would clearly be personal information.
The ICO's page on "What is personal data" says:
‘Online identifiers’ includes IP addresses and cookie identifiers which may be personal data.
The page from GDPR.EU on "Personal Data" says:
Any information that can lead to either the direct or indirect identification of an individual will likely be considered personal data under the GDPR. ... Any data that relate to an identifiable individual is personal data.
The page on "Personal Data" from gdpr-info.eu says:
Personal data are any information which are related to an identified or identifiable natural person.
The data subjects are identifiable if they can be directly or indirectly identified, especially by reference to an identifier such as a name, an identification number, location data, an online identifier or one of several special characteristics, which expresses the physical, physiological, genetic, mental, commercial, cultural or social identity of these natural persons. In practice, these also include all data which are or can be assigned to a person in any kind of way. For example, the telephone, credit card or personnel number of a person, account data, number plate, appearance, customer number or address are all personal data.
Since the definition includes “any information,” one must assume that the term “personal data” should be as broadly interpreted as possible. This is also suggested in case law of the European Court of Justice ...
See also "Can a dynamic IP address constitute personal data?"
If a hashed IP address is stored so that it can be related to a specific individual, it is personal data. as such, it would be subject to the GDPR. To store it one would need to identify a lawful basis under GDPR Article 6 This could be the Data subject's consent, or the Controller's legitimate interest. In either case the information should be included in the list of personal information collected (often in a privacy policy document), disclosed to the subject on request, adn deleted on request if possible. If that is done, such a use of a hashed IP, although personal information, would seem to be compliant.
If a hashed IP is stored in such a way that it cannot be related to any particular user, then it would not constitute personal information, and no compliance issue would seem to exist.
Limiting the retention time of a hashed IP is a good practice which would reduce any possible impact it might have.