Let me offer a different view on this...
A lot of people have been focused on how Archie’s feelings for Betty will affect Bughead’s relationship with each other and on how this could lead to Bughead’s breakup.
A point often missed by some fans is that Archie liking Betty is not tantamount to Betty also liking Archie again. I think this fact has been made very clear by how Betty had shut down any inquiry on this thrice during the last episode. The writers could not make it more obvious how she has moved on from Archie and is now hopelessly in love with our raven-haired boy.
Also, it bears noting that several different relationships will more likely be affected than Bughead’s. Actually, there have been very little talk on how Archie’s feelings for Betty will affect his relationships with first and foremost, Veronica and then Jughead. These two people will be the ones directly hurt if Archie acts on these feelings. Veronica would obviously be heartbroken and probably feel used. Jughead would feel betrayed by his supposed best friend and might decide to never let him be back in his life again. Actually, another relationship that needs to be mentioned is Archie’s relationship with the audience/viewers. This could just paint Archie’s character into even a more self-absorbed jerk who is just so pathetically oblivious on how his actions can hurt others a.k.a. this could make him even more unlikeable.