Do judges generally defer to a plaintiff's language when deciding a case or can they object to language in the original case/suit as grounds for dismissal?
It depends largely on what stage the case is at.
If the defendant has moved to dismiss the case for failing to state a claim, judges are obligated to view the facts in the light most favorable to the plaintiff. In other words, they essentially have to take the plaintiff's version of the facts as true for purposes of deciding the motion.
If the case is at the summary judgment stage (basically one or both sides arguing for a decision in their favor based on the papers they have presented), judges can only decide the case on what the undisputed facts are at that time. If there are factual matters still in genuine dispute, and those matters are material to the decision, the judge will not decide the case and will send it to trial.
At the trial stage, factual matters are sussed out and the judge decides whose versions of the facts to accept based on documents, testimony, credibility, etc.
In the Priests For Life case (the one we're talking about here), the case had already been decided against the plaintiffs by a panel of non-Kavanaugh judges, and the plaintiffs had sought a second hearing in front of a complete panel that would have included Kavanaugh. It was only at this point that Kavanaugh had an opportunity to write in dissent from the rest of the court's decision to deny a re-hearing. By that point, the facts on what the ACA requires employers to cover had already been determined, and Kavanaugh wasn't stupid enough to pretend in front of his colleagues that it was all "abortion inducing drugs." He reserved that sort of stupidity for Ted Cruz and those of us watching his confirmation hearing.