There are already laws against speech the government doesn't like. It called the "civil rights act".

from title 7:

It shall be an unlawful employment practice for an employer, labor organization, employment agency, or joint labor-­management committee controlling apprenticeship or other training or retraining, including on­-the-­job training programs, to print or publish or cause to be printed or published any notice or advertisement relating to employment by such an employer or membership in or any classification or referral for employment by such a labor organization, or relating to any classification or referral for employment by such an employment agency, or relating to admission to, or employment in, any program established to provide apprenticeship or other training by such a joint labor­-management committee, indicating any preference, limitation, specification, or discrimination, based on race, color, religion, sex, or national origin

If that is "constitutional" why wouldn't a ban on abortion sites be?