I gave up on anarchism due to sheer disappointment in humankind, but I agree: I'd say that every person who believes in democratic and humanistic principles should support the right to die.
Human dignity is the founding principle of democracy and humanism, seeing people as ends in themselves and not just means to an end, and autonomy is at the essence of that dignity. Who are we to impose our concept of dignity on a fellow innocent human? What gives anyone the right to tell someone else how to feel and what should the meaning of their life be? The protection of minorities and the underprivileged is also a keystone of democracy, that should mean effective and accessible mental health care, but it should also mean listening those who don't have a voice: if 99% of people say life is worth living, then the 1% who think it isn't should be respected as long as they don't violate anyone else's rights.
Some people don't want to admit that their views on certain topics are incompatible with their basic values. They pretend to be liberal, but oppose abortion; they call themselves feminists, but mistreat transgender people. It takes guts to live your values and uphold them with coherence because it may involve admitting certain ideas you'd initially be against. But isn't that what democracy is about? Leaving space for things you might disagree with so long as they don't threaten the very system that creates that space?