It is not easy to say which is more dangerous for the Catholic faith: an open attack or a sincere and friendly alternative offered by people of goodwill. I speak as a former anglo-catholic who studied and worshipped in tge same places as Newman.
It depends, the former is direct and the latter is indirect. If you ask me, the latter appeals to the non-scholarly. For instance, telling others that the church you go to have modern worship music or a solid bible study, people will be more open to exploring other churches. The former appeals to the scholarly. If others debate and manage to find a flaw in your reasoning, then it will encourage you to go find out about the other person’s church.
Sola Fide is just a slogan, maybe poorly framed to fit with the other Solas. Together with Sola Scriptura, it is the most ambiguous one. That surely is a problem.
A video by bluecollarcatholic, mentioned this, in the joint declaration on the doctrine of justification between catholics and lutheran have came to an understanding on this:
"We confess together that sinners are justified by faith in the saving action of God in Christ. By the action of the Holy Spirit in Baptism, they are granted the gift of salvation, which lays the basis for the whole Christian life. They place their trust in God’s gracious promise by justifying faith, which includes hope in God and love for him. Such a faith is active in love and thus the Christian cannot and should not remain without works. But whatever in the justified precedes or follows the free gift of faith is neither the basis of justification nor merits it " → Joint Declaration on the Doctrine of Justification (1997)
So, the huge disagreement would be the operational definition, rather than the result of it. Personally, I just find the protestant view of sola fide to be confusing, but many I known have came to accept this as part of their christian life.
The issue I see is that Protestantism has steered away from complex theology and more into spiritualism and pietism. These ideas surely are nice, but much of the confusion we see today comes from people who were simply too poorly catechized in what they actually believe and are more concerned with good feels.
I was raised in a feel good pentecostal church, so I have to admit that there are many who attend based on emotional assent. My mother had a church group leader who left the church during the recession after being retrenched from his job and cannot understand why God caused him to be retrenched. And usually, these leaders are meant to minister to 10-20 members. This wasn’t all, my family started to veer away from the faith altogether and stopped going to the pentecostal church. For this reason, it set me on a journey to discover the catholic faith, as I wanted to find a genuine faith as illustrated in early christianity in Acts 2, where each day, they devoted themselves to apostle teaching, fellowship, breaking of bread and prayer (Acts 2.42).