[0] Technically a distinct entity from the British royal family, it "just happens" to currently contain the same members and have similar (but not the same) succession rules.
It also gives me this silly vision of Harry at the YVR immigration counter holding up a $20 note and saying, "Because my grandma says so."
Canadian Royal Family:
https://www.canada.ca/en/canadian-heritage/services/royal-fa...
His Royal Highness The Duke of Sussex, Prince Harry:
https://www.canada.ca/en/canadian-heritage/services/royal-fa...
Her Royal Highness The Duchess of Sussex, Rachel Meghan Markle:
https://www.canada.ca/en/canadian-heritage/services/royal-fa...
But in all seriousness, immigration is a separate issue. Being a member of the royal family, unless your are the Queen herself, does not guarantee you any rights in Canada, including right of entry.