In the oracle documentation it is said
...A backslash character (\) can be used to escape special characters, such as a quote (`) or a percent character (%)...
But they are not giving full list of the special characters (or at least I couldn't find it)
The problem here was very simple - I was not escaping the brackets - ( and ). So, the log filter should look like this:
NOT(MESSAGE LIKE '%java.sql.SQLIntegrityConstraintViolationException: ORA-00001: unique constraint \(SOME.UQ_MY_CONSTRAINT\) violated%')