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FWIW, it is possible that, in these wild days, we are naturally inclined to read something into this section that is not actually there.  I may come to see what others now see, but, at the moment, I just see him saying, roughly:

"There is a common enemy that is about finish the job of enslaving all of us.  We need to set aside various differences for the time being or we will all be toast.  Yes, we have our differences, but acrimonious discussion of them does not help anyone at this late stage of the game -- as it unnecessarily exacerbates a division that the common enemy is using to conquer us all."

I am NOT saying this perspective is or is not the BEST approach -- but that this is how I read the portion in question.  IOW, I see the advocating of mutual assistance on a temporal level in order to effectively resist a common enemy, but I do not see that the author is advocating any kind of religious union or cooperation.  MP seems to be saying, "However substantially we disagree about certain things, we will all soon be toast if we do not work together in order to expel/eliminate the common threat."

I am quite open to being shown that my understanding of MP's meaning is wrong.  Further, I totally understand that there really is no solution outside of that which the Church has always taught.  Our MAIN problem IS, in fact, spiritual and, therefore, all other measures will, in the end, amount to nothing, should we fail to be converted in heart.  In that sense, this passage might be tainted with a naturalistic perspective, but that is not the same as actually and openly advocating inter-religious dialog.  One might argue that such a perspective is a step in that direction, but that does not equate to having already arrived at said destination.

I have to disagree here; the quote (and I admit I'm reading it out of the context of whatever may surround it) reeks of the heresy of Americanism, which itself is a species of indifferentism.  He's saying, it seems to me, that stark religious debate is a hindrance to the "political uniting of peoples."  This erroneously presupposes that viable political unity between Catholics and people of other faiths is possible, especially in a level of equality.  If there is something that the failed American experiment has taught us, it is this kind of silent apostasy for the sake of political expedience inevitably leads to the rise of secular political atheism, whose attacks are ever aimed at the Church and her immutable truths.

We must labor in hope of peaceful solutions between men but we must not tolerate the pride that such peace comes from the natural works of man, nor suffer under the false desperation that Jєωιѕн imperialism, or any other philosophy, religion or institution will ever triumph over God or His Church in the final analysis, no matter how grave a threat it may temporarily represent.  The endgame was written before the pillars of creation had yet been erected.  In that context, we are obligated to establish the social reign of Christ the King in all lands, for all times, regardless of how politically inopportune it might seem.  Cooperation among men comes first and only in establishing the political reality of Christianity as first and exclusive recognized by the temporal state, then allowing non-Christians limited worship in charity, while evangelizing them as we are able.  That, as a matter of historical fact, is the only means of fostering the brotherhood, procuring the peace and stamping out those heresies that threaten the Church of Christ.

We must labor in hope of peaceful solutions between men but we must not tolerate the pride that such peace comes from the natural works of man, nor suffer under the false desperation that Jєωιѕн imperialism, or any other philosophy, religion or institution will ever triumph over God or His Church in the final analysis, no matter how grave a threat it may temporarily represent.

Agreed.  Based upon this point, I think it is fair to say that the portion quoted expresses a certain lack of supernatural faith and hope.  However, that is not the same thing as advocating inter-religious dialog, which was the question in the OP.