No they aren't. There's no substantial proof for it, and the body of people who are behind this label (IARC) aren't even a food safety body. They once tried to say eating red meat is "possibly" cancer-causing as well.
They once tried to say eating red meat is “possibly” cancer-causing as well.
Because it is. Whether the effect size is significant to you or not is one thing, but there is good evidence that it has a nonzero effect. Which is similarly the case here: there is evidence of effect of aspartame, but whether the effect size is significant is up to you to decide (or legislators).