Can a user with readonly access change SQL server settings
Both the settings that you have mentioned in the question requires membership in public role, which is true in almost all the cases. You may refer below screenshot from the login window:



Kindly refer microsoft site for both of these as below:

https://docs.microsoft.com/en-us/sql/t-sql/statements/set-ansi-warnings-transact-sql?view=sql-server-2017

https://docs.microsoft.com/en-us/sql/t-sql/statements/set-arithabort-transact-sql?view=sql-server-2017

You may also refer article from Pinal Dave on this setting. There is another wonderful article from Mr. Ahmad Yaseen,

I hope above helps.