When I work on a card, it happens that I want to share my screen with people, but I don't want that people can read other cards in the background.
A solution can be to open a card in "fullscreen".
Another is to clic on a button to "hide" the background, or blurr it.
I'm glad to pass a vote along for this on your behalf, however to be candid I'm thinking that it's not something our product team would be able to prioritize in the near-term.
As a potential workaround, you could use the board's filter feature to search for just that one card by name or use a specific label to designate cards for your presentations. That way, you could search the board for just the cards that you don't mind people seeing.
Searches stay in place until you dismiss them. For example, I'm using the sky blue label to allow only one card to show on my board:
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