A Georgia trial court imposed such a ban in 2007; the Georgia Supreme Court just set it aside on Monday, in Mongerson v. Mongerson:

There is no evidence in the record before us that any member of the excluded community has engaged in inappropriate conduct in the presence of the children or that the children would be adversely affected by exposure to any member of that community. The prohibition against contact with any gay or lesbian person acquainted with Husband assumes, without evidentiary support, that the children will suffer harm from any such contact. Such an arbitrary classification based on sexual orientation flies in the face of our public policy that encourages divorced parents to participate in the raising of their children, and constitutes an abuse of discretion. See Turman v. Boleman, 235 Ga. App. 243, 244 (1998) (abuse of discretion to refuse to permit mother to exercise visitation rights with child in the presence of any African-American male); In the Interest of R.E.W., 220 Ga. App. 861 (1996) (abuse of discretion to refuse father unsupervised visitation with child based on father's purported "immoral conduct" without evidence the child was or would be exposed to undesirable conduct and had or would be adversely affected thereby). In the absence of evidence that exposure to any member of the gay and lesbian community acquainted with Husband will have an adverse effect on the best interests of the children, the trial court abused its discretion when it imposed such a restriction on Husband's visitation rights.

Two justices (Melton and Carley) "write separately to emphasize" that the quoted passage above "should only be read to stand for the well-settled proposition that, absent evidence of harm to the best interests of the children through their exposure to certain individuals, a trial court abuses its discretion by prohibiting a parent from exercising their visitation rights while in the presence of such individuals (in this instance, Husband's homosexual partners and friends)."

By the way, here's an extract from the 1998 Turman case, which I hadn't heard of it until now:

Turman and Boleman were divorced on November 13, 1996. Their settlement agreement, which was incorporated into the final judgment and decree, provided that Boleman would have custody of their minor child. The agreement gave Turman certain specified visitation rights away from the father's residence "on the condition [that] at no time shall [the child] be in the presence of William 'Larry' Little or any other African-American male except that [Turman] shall not be in contempt of court if she has casual contact with any African-American male other than William 'Larry' Little." After Turman married Kenneth Turman, an African-American male, Boleman refused to allow Turman to visit with the child away from Boleman's residence. Turman moved to hold Boleman in contempt for refusing to allow her to exercise her visitation rights. At the hearing on the contempt motion, Turman argued that the provision in the settlement agreement conditioning her visitation rights upon the child's having no contact with any African-American male was unenforceable.

The trial court improperly upheld the validity of the visitation provision which prohibited the child's contact with any African-American males. This provision is unenforceable as against public policy.... The visitation provision here violated the express public policy against racial classification and the public policy encouraging a child's contact with his noncustodial parent.

The trial court held that the provision was enforceable because it was a matter of private contract. However, after that private agreement was incorporated into the trial court's order, enforcing the private agreement became state action.... The courts of this State cannot sanction such blatant racial prejudice, especially where it also interferes with the rights of a child in the parent/child relationship.

The agreement between the parties clearly violated the State's public policy to promote the best interests of the child. "It is the express policy of this state to encourage that a minor child has continuing contact with parents and grandparents who have shown the ability to act in the best interest of the child and to encourage parents to share in the rights and responsibilities of raising their children after such parents have separated or dissolved their marriage." Contrary to this policy, the agreement prevents the child from having contact with his natural mother solely on the basis of an arbitrary racial classification. Although a court may validly provide, under appropriate circumstances, that a child is to have no contact with particular individuals who are deemed harmful to the child, such provision cannot be based solely upon racial considerations, as such ruling violates the public policy of the State of Georgia.

Monday's Mongerson, with which I began the post, apparently doesn't have this extra twist of an initial agreement by the parties; the father seemingly either never agreed to the "[no] exposing the children to ... homosexual partners and friends" condition, or agreed to it only because the trial court "express[ed] its opinion that, but for the agreement, the trial court would not have permitted Husband the limited contact to which the parties agreed" (and then promptly appealed the trial court order).

Thanks to How Appealing for the pointer.