According to the traditional viewpoint, you're "supposed" to find a posek and abide by his rulings. But let's be honest. In practice, especially in the internet age, many people shop around for a halachic ruling that they're comfortable with.
Is this so terrible? While I'm sure that some shop around just so they can engage in practices that they'll enjoy, I suspect that most do so for practical reasons, because their lives would be much more difficult if they had to rely only on their local rabbi. Especially in the last several decades, when compassionate kulot (leniencies) are much less part of your average Orthodox rabbi's toolkit than they used to be.
So people turn to the internet. They don't want to just violate halacha, but they sometimes desperately need a lenient ruling, whether it be for something as benign as a pressing business need or as serious as a sick family member. So they ask people in Jewish discussion groups, or look around at various responsa online.
Aside from the fact that this allows for them to find compassionate rulings, this practice can be good for another reason. It's people taking their halachic lives into their own hands, asserting their autonomy, and engaging much more deeply with halachic reasoning than if they just asked their shul rabbi.
Yes, there's certainly potential for abuse, and anyone who seeks a psak that they are more comfortable with has to be very self-aware of their motives. But on the whole, I think this is a positive development.