Hmm... Since your description is pretty vague, my opinion would be (as alpha1 rightly said) that it again depends on who the people in question is.
For example, assume you were considering music as a career and wish to take up a music degree from a premier university (think Berklee) because that's what your heart tells you to. Now the opinions that matter would be that of your parents' and family - because they share the consequences of your decision. Also, those of people who have completed such a course matter. Opinions of people like us in an internet forum needn't be the deciding factor because we have neither a clue about how hard your determination is to get through it nor the first hand experience to advice you. Take such opinions with a pinch of salt.
Another example - should an artist care about what their audience think when they perform? I personally think that they should because the fans are paying money (directly or indirectly) for it. Its okay to get a little edgy at times but to play a gig when you haven't prepared well for it or when you are piss drunk is just disrespectful. On the other hand, fans have no right to judge the artist by his personal life.
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