The significance of the discussion about what they should drink is its insignificance. By reading between Hemingway's minimalistic lines, we realize Jig is pregnant and the American man is desirous of her getting an abortion. We also realize her sentiments lean the other way--that is, against an abortion--even though she plainly says, "I'll do it. ... then everything will be fine." So, here they are, faced with a monumental problem that involves a potential new life and all they can manage between themselves by way of conversation is what they should drink. This indicates how distracted by the situation each is from the enjoyment of normal living.
It also reveals an ironically deep shallowness to their relationship, which Jig points out and describes succinctly when she says: "That’s all we do, isn’t it – look at things and try new drinks?" Jig is trying to be "amused" and to have "a fine time" but this shallowness continually shows up. The man shallowly says, "I know you wouldn’t mind it, Jig. It’s really not anything," then "But I don’t want anybody but you." Jig herself expresses the shallowness of their relationship when she says, "it will be nice again if I say things are like white elephants, ...."
In summary the significance of the conversation about what to drink is (1) its very insignificance as it covers up the truly significant problem they must face and that (2) it illustrates the shallowness of their relationship.
'They just let the air in and then it’s all perfectly natural.’
‘Then what will we do afterwards?’
‘We’ll be fine afterwards. Just like we were before.’
‘What makes you think so?’