SQL How to join 2 tables with or without

Remove the additional unnecessary join to contact:

SELECT 
    Person.Id,
    Person.Name,
    GroupedContact.MaxDate as outputCol

FROM
    Person
    LEFT JOIN (
        SELECT      Contact.PersonId, 
                    MAX(Contact.Date) AS MaxDate
        FROM        Contact
        GROUP BY    Contact.PersonId
    ) GroupedContact ON 
        Person.PersonId = GroupedContact.PersonId

A few notes: Never mix implicit and explicit joins. Always use explicit joins. You need here a LEFT join which means -> keep all the records from the LEFT tables and those that match from the RIGHT table.

You need LEFT join instead of RIGHT and extra join to contacts is not needed:

SELECT 
    Person.Id,
    Person.Name,
    GroupedContact.MaxDate
    
FROM Person
LEFT JOIN 
(
    SELECT      Contact.PersonId, 
                    MAX(Contact.Date) AS MaxDate
    FROM        Contact
    GROUP BY    Contact.PersonId
) GroupedContact 
  ON Person.Id = GroupedContact.PersonId