This is an interesting question, and I think once again one's response as a Protestant depends on whether you are in the Reformed/Calvinistic or Arminian camp.
As a Calvinist, I think the Bible teaches to preach the gospel, not to save souls. I have no desire in getting someone to say a prayer, and then telling them: if you were sincere in what you just prayed, then you are now saved. What does that sincerity mean? I think it means if you just didn't pray to get rid of me, then it was sincere. But people can pray sincerely because they seek what God offers (e.g., peace), not because the have been regenerated by the Spirit and seek God Himself. In that case, they are sincerely wrong.
No doubt many have come to Christ in this manner. However many others have experienced momentary euphoria based on a false assurance.
Getting back to Catholics. I have said many times on this blog that I feel a closer kinship to Catholics than to many Protestants. I think they are seriously in error, but I also think that they recognize that truth is absolute and there is no compromise when it comes to the gospel (they just haven't gotten it right, which is what they would say about me.)
Ironically, the most virulent anti-Catholic bigotry comes, in my opinion, from fundamentalist Arminian churches. These tend to zero in on important but secondary issues such as "The Immaculate Conception". On the vital soteriological question, Arminians and Catholics are in virtual agreement. For example, from The Council of Trent, on the canons concerning justification, we read:
Canon 4. If anyone says that man's free will moved and aroused by God, by assenting to God's call and action, in no way cooperates toward disposing and preparing itself to obtain the grace of justification, that it cannot refuse its assent if it wishes, but that, as something inanimate, it does nothing whatever and is merely passive, let him be anathema.This is the crux of the Catholic response to the Reformer's teaching on sola fide. It is also the modern Arminian position, although most would be loath to admit that in the debate between Rome and Martin Luther, they fall squarely in the Catholic camp.
Canon 9. If anyone says that the sinner is justified by faith alone, meaning that nothing else is required to cooperate in order to obtain the grace of justification, and that it is not in any way necessary that he be prepared and disposed by the action of his own will, let him be anathema.
That is worth repeating. In the issue that was at the heart of the debate between the Reformers and the Catholic Church, the overwhelming majority of conservative Protestants (which is the Arminian camp) stand in agreement with the Catholic church. Those of us who agree with the Reformers are a minority.
So what does this all mean when it comes to evangelism? Well to me, I will always teach the gospel to a Catholic, just like to anyone else. That is how I evangelize. The Catholic may not even recognize what I am doing as evangelism. It probably looks more like friendly debate. I would never try to get a Catholic to say the sinner's prayer. Then again, I would never try to get anyone to say it.
I have no problem supporting missionaries in predominantly Catholic countries, for I think they have been taught an incorrect gospel. We are instructed, under threat of eternal damnation, to teach not just any nice-sounding gospel, but the correct one.
On the flip side, but by the same reasoning, Catholics should be evangelizing me. It would not insult me if they tried to "sheep-steal" me. I would respect them for it.