This dovetails nicely into a discussion that was recently had regarding whether man's participation in natural law is always sufficient for him to be called moral. I posited that, in those cases where the observance of natural law does not come in the service of a religion or cultural affectation that is inimical to the true Christian religion, such a thing could be meritorious to a degree. However, when those things are done in observance of a false religion, and especially to establish that person in obstinate belief and participation of it, I would argue that such a thing is odious to God.
However much Protestantism may superficially resemble the Catholic faith, which is uniquely and integrally the divinely revealed religion of God, it is substantially false. It worships as its central figure and Person of the Godhead (and even the latter is variable; in Unitarian Protestantism there are no persons, and in Mormonism He is not God at all) a version of Christ that is objectively and historically untrue, and ascribes to Him a theology that is alien to the true faith. The simple acceptance of Jesus Christ as Deity and a vague or totally incorrect notion of His role as the propitiation of all the sins of mankind is, in my estimation, insufficient to be considered the exercise of Christian faith. I would further argue that prayers offered in the service of false religions, however well-meaning they might be, are still done in service of a religion that is objectively false. To say otherwise, would be no different than to say that the prayers of a Moslem, whose false religion nonetheless places Jesus Christ as the greatest prophet of God, even above the Mohammed himself, are efficacious and pleasing to God.
A prayer is an expression of the interior spiritual life, which begins and ends in the service of that religion to which that spiritual life is dedicated. The prayer as one of the most fundamental expressions of that religion must, I think, rightly be presumed to fall under the species of virtual intention to practice a false religion, insofar as the prayer, though not presently explicitly dedicated to a religion inimical to God and His true Church, nonetheless follows from a prior intellectual assent to the truth and efficacy of the same.
Against, this is just my own opinion.