Most Protestants I happen to know (and probably most Catholics, too) are not hung up on infallibillity. In other words, they hold the general view that nobody knows the ultimate truth about certain ultimate questions, that there is no one true church, that we should maintain some humility when it comes to understanding this mammoth, magnificent, miraculous and mysterious universe.
Take mainline Protestants as a whole. I don't find Methodists, Presbyterians, Episcopalians, members of the United Church of Christ and other arguing that they belong to the one true church or that they have some sort of monopoly when it comes to valid doctrine. They have little differences - maybe in liturgy - but years ago they seem to have reached the point of agreeing to disagree. And even among those in the same denomination.
An illustration. Attend an ecumenical Bible study and Protestants may take issue with one another on this or that verse, but nobody pulls out a catechism to 'prove their point'. No, they permit and even seem to encourage individual thinking. This had led to many denominations, true, but does give members considerable intellectual freedom.
And, as said already, most Catholics I know well (there are exceptions) seem to feel similarly. Many of them take issue with the church on - for example - ordination of women, perhaps, or artificial birth control, and even on such sacred and central beliefs as transubstantiation or the sinlessness of Mary. Whether the hierarchy recognizes it or not, vast numbers of Catholics remain in the church for family or cultural reasons who do not agree on major matters. I believe a survey in the *US Catholic* magazine awhile ago found that 43% of Catholics confessed that they did not believe in transubstantiation.
If people need or want a church that claims infallibility in theological and moral teachings, Catholicism may be it. Although there are millions of evangelical Protestants who claim that they alone embrace the truth, not by belonging to any particular denomination, but having been saved by their faith in Christ.
Lots more to say, but tempus fugit.