Compelled speech?

[Volokh, Eugene]

The ACLU reports (http://www.aclu.org/LesbianGayRights/LesbianGayRights.cfm?ID=14999&c=101) that it helped a gay man file a complaint against a business for refusing to print invitations to a gay wedding; the printer was in Seattle, and Seattle law prohibits sexual orientation discrimination.  The business owner settled, "acknowledg[ing] that all persons should be treated with respect and dignity, regardless of sexual orientation," "apologiz[ing] that her actions offended and hurt Butts," and "agree[ing] not to violate Seattle's anti-discrimination law in the future."
 
Say the case hadn't settled, and the complainant had prevailed.  Would this have violated the business owner's rights to be free of speech compulsions?  Note that the business owner isn't just being required to, say, serve food to someone, or even rent a residence to someone -- the business owner is being required to participate in the printing of material whose content she finds offensive.
 
A follow-up question:  Seattle law also prohibits discrimination based on political ideology (defined as "any idea or belief, or coordinated body of ideas or beliefs, relating to the purpose, conduct, organization, function or basis of government and related institutions and activities, whether or not characteristic of any political party or group").  Say that someone files a complaint against a pro-gay-rights printer for refusing to print leaflets urging the criminalizing of homosexual conduct (a belief relating to the conduct of government), or a pacifist printer for refusing to print material urging war.  May the Seattle Office for Civil Rights order the printer to print such material, or fine the printer for not printing such material?  Or would this violate the printer's rights to be free of speech compulsions?
 
Eugene