Once again ... I am NOT (by the Grace of God) a lawyer .. but my immediate answer would be NO. However, anyone can file any frivolous suit they want for any reason. An unfortunate number of suits are filed purely for harassment ... even the most unfounded suit, once filed and served, has to be answered. Typically that involves hiring a lawyer. Even more typically that costs time and money.
HOWEVER, that lawyer would immediately file to dismiss the case as frivolous and would likely win the dismissal, including the costs of defending the frivolous action.
Most lawyers would not file such a suit in the first place, knowing the case would be dismissed, so usually that kind of totally frivolous suit is filed by an individual proceeding on his/her own.
Civil suits that would attempt to restrict your constitutionally protcted freedoms, taking into account your stated restrictions, would or should be dismissed rather quickly. (I say ‘should’ because there are a number of judges who I would not trust in this regard).
That is why the Snyders didn’t sue about the protests themselves. Their attorneys undertood that the Phelps crowd has a right, within the restrictions set out about protesting at funerals, to say the most obnoxious things possible. They don’t have the right to defame. The lawyers knew the difference and sued accordingly.
Does this include theological statements? A precedent like that could come back and bite mainstream fundamentalist Christians, or even mushies who still believe there is a hell and that some people go there.