An important clarification - while LDS believe the Catholic Church is apostate, we DO NOT BELIEVE the Catholic Church is FALSE (False implies there is nothing good or right.)
LDS believe other Christian faiths have part of the message but not the whole message.
In as much as they are teaching the word of God, they are doing good in this world.
That is not consistent with this LDS teaching:
“She is termed, in other places, by the same prophet, “The whore of all the earth,” making the nations drink of the wine of the wrath of her fornication. Some three centuries ago there came out sortie excellent men, named Martin Lather, John Calvin and many others that might be mentioned, who protested against the wickedness and abominations of the Church wherein they had been educated, and of which they had been members. Because of their protestations against the mother Church they were called Protestants. They pronounced her the whore of all the earth; they declared that she had no authority, that she had none of the blessings and gifts which characterized the ancient Christians. They came out and established other Churches… But among all these Churches where are the characteristics of Zion? We hunt for them in vain.”
- Apostle Orson Pratt, Journal of Discourses Vol. 14, p.346
D&C 29:21:
“And the great and abominable church, which is the whore of all the earth, shall be cast down by devouring fire, according as it is spoken by the mouth of Ezekiel the prophet, who spoke of these things, which have not come to pass but surely must, as I live, for abominations shall not reign.”
D&C 88:94:
“And another angel shall sound his trump, saying: That great church, the mother of abominations, that made all nations drink of the wine of the wrath of her fornication, that persecuteth the saints of God, that shed their blood—she who sitteth upon many waters, and upon the islands of the sea—behold, she is the tares of the earth; she is bound in bundles; her bands are made strong, no man can loose them; therefore, she is ready to be burned. And he shall sound his trump both long and loud, and all nations shall hear it.”
- The Church has a history of identifying the Catholic Church as the great and abominable church.
"The present Christian world exists and continues by division. The MYSTERY of Babylon the great, is mother of harlots and abominations of the earth, and it needs no prophetic vision, to unravel such mysteries. The old church is the mother, and the protestants are the lewd daughters. Alas! alas! what doctrine, what principle, or what scheme, in all, what prayers, what devotion, or what faith,
since the fathers have fallen asleep,' has opened the heavens; has brought men into the presence of God; and to the spirits of just men made perfect, and to an innumerable company of angels? The answer is, not any: There is none in all christendom that doeth good; no, not one.’
- Apostle John Taylor, Times and Seasons, Vol.6, No.1, p.811
“Babylon, literally understood, is the gay world; spiritual wickedness, the golden city, and the glory of the world, The priests of Egypt, who received a portion gratis from Pharaoh; the priests of Baal, and the Pharisees, and Sadducees, with their “long robes,” among the Jews, are equally included in their mother’s family, with the Roman Catholics, Protestants, and all that have not had the keys of the kingdom and power thereof, according to the ordinances of God.”
- Prophet John Taylor, Times and Seasons, Vol.6, No.1, p.939
"Both Catholics and Protestants are nothing less than the “whore of Babylon” whom the Lord denounces… as having corrupted all the earth by their fornications and wickedness. And any person who shall be so wicked as to receive a holy ordinance of the gospel from the ministers of any of these apostate churches will be sent down to hell with them, unless they repent of the unholy and impious act. If any penitent believer desires to obtain forgiveness of sins through baptism, let him beware of having any thing to do with the churches of apostate Christendom, lest he perish in the awful plagues and judgments, denounced against them. The only persons among all nations, kindreds, tongues, and people who have authority from Jesus Christ to administer any gospel ordinance are those called and authorized among the Latter-day Saints. Before the restoration of the church of Christ to the earth in the year 1830, there have been no people on the earth for many generations possessing authority from God to minister gospel ordinances. We again repeat. Beware of the hypocritical false teachers and imposters of Babylon!
- Apostle Orson Pratt The Seer, Vol.2, No.4, p.255
exmormon.org/mormon/mormon327.htm
I think it’s important to respect each others beliefs and certainly encourage the good aspects of other religions. I believe God does not abandon us just because we see him in different ways, through different religions.