Unable to leave random steam groups
When you ask Steam to follow a game, you receive that game's announcements in your activity feed. Not explicitly mentioned, or at least not where I could find it, is that you also join that game's official group. When you stop following a game, you will automatically be removed from the group, meaning that any rewards or advantages that require you be a member will no longer be available.
Official groups are not counted in the number of groups you're a member of; this was already the case before the introduction of following games and the discovery queue.
You can leave such a group in two ways:
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Go to the game's store page and untick 'Following':
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Go to your game's community hub, and click the 'Stop Following' link near the top: