Well Twitter moved back their v1 API shutdown, but yesterday (June 11th) it was turned off for good.
As far as I understand the limits of a Shopify theme, it doesn't seem like it's going to be possible to have a custom Twitter feed anymore. I'm interested to hear what they have to say about it.
EDIT: As they pointed out below, you can use an embedded Twitter feed from their website but you can't skin it very much.