A public high school student newspaper for many years has accepted advertising from local businesses to help pay the costs of publishing the paper.  The school has no written policy on what ads it does and does not accept, but it has never turned down any ad before the incident described below.

The faculty advisor to the paper has refused to allow the newspaper to publish an ad from a local Planned Parenthood clinic that states its location and the services it provides which include gynecological exams, birth control, pregnancy testing, and pregnancy counseling and referral. The advisor explains his decision on the ground that the school does not want to encourage sexual activity among its students and Planned Parenthood provides contraceptives to teenagers.  He argues that an ad in the paper promoting access to contraceptives will undermine the school’s abstinence policy.

Planned Parenthood sues the school on the ground that the decision to reject its ad violates its First Amendment rights.  What result and why?