The federal court will abstain. It’s called the Younger Abstention Doctrine. Younger v. Harris, 401 U.S. 37, 91 S. Ct. 746, 27 L. Ed. 2d 669 (1971).
Younger was used in Canatella v. California, 404 F.3d 1106, 1109 – 1110 (9th Cir. 2005) by the federal court to dismiss a case where an attorney sought to have the court address certain First Amendment issues regarding the bar association’s interest in disciplining him:
The Middlesex Factors: “Absent `extraordinary circumstances’, abstention in favor of state judicial proceedings is required if the state proceedings (1) are ongoing, (2) implicate important state interests, and (3) provide the plaintiff an adequate opportunity to litigate federal claims.” Hirsh v. Justices of Supreme Court of Cal., 67 F.3d 708, 712 (9th Cir.1995) (per curiam) (citing Middlesex County Ethics Comm. v. Garden State Bar Ass’n, 457 U.S. 423, 432, 437, 102 S.Ct. 2515, 73 L.Ed.2d 116 (1982)).
A good discussion of these matters is to be found in Joshua G. Urquhart, Younger Abstention and Its Aftermath: An Empirical Perspective, 12 NEV. L.J. 1, 2 (2011-2012):
The Ninth Circuit ran through the Younger analysis and held: (1) the state bar case constituted an ongoing judicial proceeding; (2) regulating attorney misconduct was an important state interest; and (3) Bendel had adequate opportunity to assert his federal defenses in a competent and unbiased state forum. The court thus upheld the abstention decision and affirmed the denial of the intervention motion. 8 [Canatella v. California, 404 F.3d d. at 1117].
The Younger Abstention Doctrine might be in for some revision in light of Sprint Communications, Inc. v. Jacobs, 134 S. Ct. 584, 187 L. Ed. 2d 505 (2013). See, Supreme Court Narrowly Defines Younger Abstention Doctrine, ABA Litigation Section, February 14, 2014.