Does being an alpha and omega considered a straight couple when they're in a relationship ...

Socially, yeah
I could write an entire thesis on how the real life patriarchy based on who gets pregnant and how this seeped into "misogyny toward men" in omegaverse

Depends on the story. Sometimes yes, sometimes no. In some manhwa they're still considered gay relationship because alpha and omega are subgenders and in others alpha x alpha is considered as same sex relationship.