Astrology is almost certainly right in some respects (a stopped clock is right twice a day after all). Other than time of birth thing, I suspect some of the personality traits astrology describes are genuinely traits that humans can have (although, I'm not actually familiar with what astrology describes), they just don't correlate to birthdate/planet as claimed. Astrology was after all created by humans are familiar with human behaviour.

Regarding birth date, I would speculate that one of the most significant effects it has on modern children is how far through the school year they are born (and thus whether they are one of the older children or one of the younger children in their cohort). As you say, it's likely that there's some effect. I personally somewhat doubt it's causes differences in personality anywhere near as drastic the kind that astrology claims.