Do I have to put up with homophobic harassment?

No- whether you identify as gay or not. Connecticut state law expressly forbids discrimination on the basis of sexual orientation, and a federal court in Iowa recently held that anti-gay harassment could violate Title VII of the Civil Rights Act of 1964 as well. In this case, the court held that anti-gay graffiti on the plaintiff’s car, being asked whether he had AIDS, and offensive touching could, if proved, violate federal law.