You can’t be a conservative without being a “cultural conservative,” because the very term itself means “someone who conserves” presumably what already exists. A conservative, therefore, would want to conserve traditional society as we had in this country for 170+ years.
bump
Your contention is not well supported by the argument you’ve presented.
It is possible to want to conserve the economic liberty the Founders provided and thereby be a conservative. Nothing requires us to want to conserve all ( e.g.Slavery) of what the Founders gave us to be a conservative.