Just let Jeph work out the kinks and figure out the dynamic more, it'll feel less awkward eventually.
This is awkward on the "teenage-crush-first-date awkward" level of the scale. Yeah, Dora could have been a little more careful with her words... but who hasn't proverbially stuck their foot so far in their mouth that they're able to kick themselves in the stomach for being so stupid?
Next strip is all about the damage control, for sure.
As another said though, it is awkward to the point of being forced a bit. As evidenced by some of the drama. Agreed on "Fayngus" though. Definitely the healthiest looking and most "organic" pairing yet.
Dora/Marten wasn't awkward to me. They/Dora just had that Faye issue in the background. Steve. Oh man. Steve is just an entirely different beast in this comic.
The awkwardness in this situation is probably based on how little they know about each other. Tai was infatuated by Dora, because of her seemingly successful life, and her solid character. Dora accepted, based on how upfront and honest Tai was about her feelings. But was it ever established, how much do they know about each other? And how much did they really interact with each other beforehand? Not a great deal on both counts, I think.
Marten and Dora happened because their interactions (particularly after "The Talk") brought them closer and closer together. They basically knew each other inside and out, and when the question of Faye was no longer a question... well, the opportunity was there for them to learn about each other from the outside in (no matter how serious a discussion on relationships, there's always time for a good (or probably bad, in this case) sex joke).
Angus and Faye. How many relationships have started out like that, in any case? Go to a coffee shop, bar, grocery store, restaurant or other eatery... anywhere where one is providing service to another, and you'll see people interacting in a similar way. They become regulars, share quips and conversations, and it ends up like they've known each other their entire lives. Worse case scenario? One or both is married or in a relationship (although that doesn't stop some people...).
This is about as "natural" as it gets these days. The customer ends up being a regular, they see that particular cashier/barista/waitress/barmaid (or barman) because they're their favourite, and off it goes from there.