What do sources say about purchasing smoothies at places with no kosher certification? Would this be allowed?
There are a number of potential issues with smoothies
- the milk or yoghurt: which might or might not be chalav Israel for those who pay attention to this
- fruit: particularly strawberries or raspberries commonly contain insects: however since they are crushed ou pureed this is not an issue (see here from R Moishe Dovid Lebovits)
- other fruit juices used if any: they would need to be kosher, with a particular issue with grape juice if handled by non-Jews
- any supplements (Wikipedia: sweeteners, whey powder, plant milk, nuts, nut butter, seeds, tea, chocolate, herbal supplements, or nutritional supplements) would need a reliable hekhsher
- the blender: in case it is used to blend other non-kosher beverages and not cleaned well
- sitting down in a non-kosher restaurant (see e.g., here): although you are maybe asking about only purchasing a drink which is permitted by some
So, in summary a cold smoothie prepared on dedicated or clean equipment, with no or kosher supplements, might be permitted if prepared with water, kosher fruit juice or, for someone not particular about chalav Israel, milk.