This is another one where Catholics have the opposite view;
Right.
they believe that personal effort is all that matters, and that a good person who does good deeds but who has never had faith in Jesus will still go to heaven.
I've found Catholicism to hold a number of beliefs that just aren't Biblical. A pathway to heaven through any sort of personal effort (good works) simply doesn't exist. It is the work of Jesus Christ (living a perfect/sinless life, suffering death on a cross, and resurrecting back to life three days later) that opened up a pathway to heaven, not anything else that anyone else has ever done.
John 14:6 states, and this is Jesus speaking: "I am the way, the truth, and the life. No one comes to the Father except through Me".
Ephesians 2:8-10 states: "For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. For we are his workmanship, created in Christ Jesus unto good works, which God hath before ordained that we should walk in them.
Matthew 7:21-23 states, and this is Jesus speaking again: "Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven. Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity."
With that being said, there IS something that a number of other Christians could learn from Catholics, and that's that good works are also an important part of Christian life (that good works are NOT meaningless, or unnecessary, or able to be overlooked, simply because they "don't result in salvation").
The Parable of the Good Atheist
One day gfm7175 and IBDaMann were sharing an Uber when a terrible traffic accident took their lives and placed them before the righteous judgement of God. gfm7175 noticed that he was standing in a long line that contained many people he knew, even a few from his church, and the line was moving rather quickly, with everybody seemingly getting waved on in. As he looked to his left, he saw that IBDaMann was in a line with a lot of people he did not recognize, and that line was moving quickly as well. gfm7175 remarked "Hey, IBDaMann, you aren't supposed to be here. You were an atheist; you can't get in here." IBDaMann answered "Not in that line, I can't. That's why I'm in the Catholic line. Their policy is that
God will render to every man according to his deeds!" , and I have already been declared a "good" athesit. See? I already got my voucher. " IBDaMann then pointed to the Catholic banner that read "
Romans 2:7 - To them who by patient continuance in well doing seek for glory and honour and immortality, eternal life:" IBDaMann then suggested to gfm7175 that he not be afraid to come to him for some good deeds.
Ha! An entertaining parable.

However, "good deeds" alone won't cut it. It is having faith in the gracious work of Jesus Christ that leads to eternal life. Jesus says that there's no other way to eternal life except through him, regardless of what the "Catholic line" (as you dubbed it) may believe.