There is confusion around the usage of the term ex-officio. The term means by virtue of your office. So an ex-officio board member holds the position on the board because of another role they fulfill. An example would be a funder who places their CEO on your board. The position on the board is for the CEO of the charity, whoever that might be. If the CEO changes at the funder then the board member changes on your board.
The ex-officio position can be voting or not. There is nothing in the term ex-officio to suggest no voting rights. Sometimes the confusion is that a person is an observer on the board. The observer role is a non-voting role. Board meetings are more effective when all the members know why they are there and who can vote.