Would it be rude to go to someone's funeral without being invited by the family?

no its a funeral not a party

if you had a relationship with that person, and they happened to just not be aware of it, no. but it would be wise to let them know ahead of time, who you are, what you meant to that person and what they meant to you, and why you would like to be there.

If you get along with the family it's probably fine to stop by just to show your respects. But if you've had conflict with these people you should let them mourn in peace.

Invitations are not extended for funerals.

Even if you hate the person you are allowed to go to pay your respects, unless u killed them, then the family wouldn't be pleased.

No you’re allowed to go to a funeral if you please.

Unless it is a private funeral, nobody sends out individual invitations. Funerals are for the living to pay their respects. If you want to go, then go. The family may be touched at the number of people who come.

No. They don't do invitations to funerals like they do with weddings and birthday parties. If you know someone in the family they might tell you there's a funeral and where and when, in case you might want to come, but that's not an invitation.

Not really. Unless you have bad intentions, you deserve a chance to pay your last respects.