It is true that in the 1856 campaign, Fillmore put the most emphasis on the threat to the Union, rather than nativism. He argued that the new Republican Party was entirely northern, that the Democrats were dominated by the South, and that if either party won, there would be a civil war--not that bad a prediction. Still, he did join a Know Nothing lodge and did endorse the Know Nothing nativist program. I don't think he was personally anti-Catholic; he had his daughter educated by nuns. But the Know Nothings were really the only game in town if you wanted to oppose the Democrats and Republicans--both of which Fillmore thought were "sectional" parties and therefore a menace to the Union.
"The Know Nothings had risen to power by crusading against old party hacks, calling for political reform, and shrewdly exploiting both anti-Catholic and anti-Nebraska sentiment so pervasive in the North. Fillmore had no interest in any of these issues. To him and the clique of Silver Grey Whigs around him, the major issue of the contest, indeed the great issue since 1850, was the preservation of the Union. In a series of short campaign speeches that he delivered following his return from Europe, Fillmore over and over again stressed the importance of the Union issue while giving only lip service to the nativist sentiments that motivated the party's rank-and-file." William E. Gienapp, *The Origins of the Republican Party, 1852-1856,*
https://books.google.com/books?id=AWtZnsxMCDEC&pg=PA441
Nevertheless, it would not be true to say that Fillmore neglected nativism altogether. Consider his Newburgh speech:
"Fellow citizens of Newburgh.— Accept my cordial thanks for this hearty greeting. My friend has introduced me as the standard bearer of the American Party, and a friend of the Union. For the former position I am indebted to the partiality of my friends, who have without my solicitation made me your standard bearer in the contest for President, which has just commenced; but I confess to you that I am proud of the distinction, for I am an American, with an American heart, (cheers). I confess also I am a devoted and unalterable friend of the Union. As an American, occupying the position I do before my countrymen, I have no hostility to foreigners. I trust I am their friend. Having witnessed their deplorable condition in the old country, God forbid I should add to their sufferings by refusing them an asylum in this. I would open wide the gates and invite the oppressed of every land to our happy country, excluding only the pauper and criminal. I would be tolerant to men of all creeds, but would exact from all faithful allegiance to our republican institutions. But if any sect or denomination, ostensibly organized for religious purposes, should use that organization, or suffer it to be used for political objects, I would meet it by political opposition. In my view, Church and State should be separate, not only in form, but fact — religion and politics should not be mingled.
"While I did this I would, for the sake of those who seek an asylum on our shores as well as for our own sake, declare as a general rule, that Americans should govern America, (great cheering). I regret to say that men who come fresh from the monarchies of the old world are prepared neither by education, habits of thought, or knowledge of our institutions, to govern Americans. The failure of every attempt to establish free government in Europe, is demonstrative of this fact, and if we value the blessings which Providence has so bounteously showered upon us, it becomes every American to stand by the constitution and laws of his country, and to resolve that, independent of all foreign influence, Americans will and shall rule America, (cheers)..."
https://archive.org/stream/mrfillmoreathome01buff/mrfillmoreathome01buff_djvu.txt
Beneath all the claims of liberality toward immigrants and belief in freedom of religion, Fillmore is expounding the nativist line. For even the Know Nothings in those days did not advocate any general restrictions on immigration (beyond "paupers and criminals"). What they wanted to do was to curb the *political power* of immigrants--and that is what Fillmore unequivocally comes out for here. ("Americans should govern America.") Moreover, without mentioning the Catholic Church by name, he also echoes anti-Catholic themes:
"I would be tolerant to men of all creeds, but would exact from all faithful allegiance to our republican institutions. [Guess which church was widely suspected of not bearing allegiance to our republican institutions?--DT] But if any sect or denomination, ostensibly organized for religious purposes, should use that organization, or suffer it to be used for political objects [once again, all nativists knew what church was being referred to here--DT] I would meet it by political opposition. In my view, Church and State should be separate, not only in form, but fact — religion and politics should not be mingled."
So Fillmore's embrace of nativism may have been opportunistic, and it was definitely a very secondary theme of his campaign, which focused on the threat to the Union. But he did embrace nativism and even--though only implicitly--anti-Catholicism.