Hi @anon13584666 and welcome to the forum,
Not with Asana natively, as Asana rules do not support triggers or actions involving tags.
You can automate it with our Flowsana integration; Flowsana’s rules have trigger conditions for “if tag X is added to a task” and “if tag X is removed from a task”, and we have rule actions for “add tag X to task” and “remove tag X from task”.