The Real Reason The Royal Family Doesn't Vote
While Queen Elizabeth II and other members of the royal family have numerous rights and privileges that do not extend to we commoners (particularly non-Brits), there is one pretty basic right that they choose not to exercise, and that is to cast their votes in a general election.
Technically the Queen, along with Prince Charles, Will, Kate, Harry, Meghan, and all the gang can vote. There is no specific law preventing them from doing so (via Mirror Online). However, according to Newsweek, it is the opinion of the UK Parliament that it would be unconstitutional for the queen to cast a ballot, and the rest of the family also choose to honor this convention rather than making waves in a most un-royal way.
Why the crown keeps out of politics
Queen Elizabeth II has always (or nearly always) held to a policy of staying above the political fray, as the British monarchy has, since the end of World War I, functioned on a largely ceremonial rather than governmental basis.
As the official royal website explains: "As Head of State The Queen has to remain strictly neutral with respect to political matters. By convention, The Queen does not vote or stand for election, however Her Majesty does have important ceremonial and formal roles in relation to the government of the UK."
She limits her involvement in each general election to meeting with the winning candidate after the election results have been announced and formally requesting that this candidate form a government on her behalf.
The rest of the royal family, while not technically bound by the same constraints as the reigning monarch, nevertheless find it easier to remain officially neutral on political matters. Any exceptions they may make could land them in controversy, as with certain letters written in 2004 and 2005 by Prince Charles to then Prime Minister Tony Blair that had him accused of meddling in policy (via PopSugar).
One time the Queen broke the rules
While throughout most of her long life Queen Elizabeth II has been a dedicated rule follower, indications are that she may be loosening up a bit in her 90s. One example occurred when she uncharacteristically spoke out about Brexit in early 2019. Although her remarks were limited to expressing a desire for civility and common ground, nonetheless there were some in the press who saw the fact of her even alluding to this political hot potato as controversial.
Why would the queen choose to break a lifetime of careful non-commenting at this juncture? Perhaps it's due to the ongoing struggle that Brexit has proven to be for the nation she leads. Marie Claire posits a cheekier theory, however: They put the queen's newfound outspokenness down to the influence of daughter-in-law Meghan Markle, who is herself no stranger to rule-breaking. Could this be so? Hmm, this bodes well for a new and very interesting era in royal-watching.