The festival has dealt with sufficient turmoil since barring the group from one of the largest events of its kind worldwide.
Hundreds of thousands of people protested across Germany against the AfD after a report that two senior party members had discussed plans for mass deportation of citizens with foreign backgrounds.
Far-right parties have gained ground across Europe but the rise of the AfD touches a particularly sensitive nerve in Germany because of the country's Nazi past.
Stephan Kramer's comments come after the Alternative für Deutschland candidate won the local district council election in the same state.
The party opposes economic sanctions against Moscow over the Ukraine war and dispute that human activity is a cause of climate change.
The spy agency said that the Young Alternatives wanted a society that was as ethnoculturally homogeneous as possible.
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