That's what my parents worry about except my mum worries about Mandarin whilst my dad worries about Hakka so we speak 2 different languages at home because we speak English with our friends but I know that I'm chinese and having an English accent doesn't change anything.
i really think that whatever a person speaks is highly influenced by whatever language/culture is dominant in the person's life... but regardless, people nowadays should at least know english and mandarin; they're like the major languages of the world