Seems like especially at the time there would have been a lot of racial tensions building up specially with an interracial couple be married on television.
Were Hispanic people with no visible non-European ancestry considered non-white at this time?
Back then (and until surprisingly recently) there was cultural disapproval of intermarriage between religious groups. Lucille Ball being a Protestant, and Desi being a Catholic may have encountered family and community friction.
Their mutual cultural upbringings would have differed moderately in a pre-television world. I would however guess that the "showbiz" community that they were more directly a part of would have been much more accepting.