There is an issue where if you have both the Variant Dropdown and the Radio Button Variant Picker (known as Basic in the Variant Column) in the same section (or page), the Variant Dropdown malfunctions.
You have to manually delete the Radio Button Variant Picker, for the Dropdown to work. Even if you have turned of visiblity on the Radio Button.
This is something that probably has to do with Shopify, because in the Instant builder it does work without deleting it.