The tax collector simply repented, as did the thief on the cross. In the case of the woman, Jesus Himself said it was her FAITH that saved her.
Luke 7:39-50 39Now when the Pharisee who had invited him saw this, he said to himself, "If this man were a prophet, he would have known who and what sort of woman this is who is touching him, for she is a sinner." 40And Jesus answering said to him, "Simon, I have something to say to you." And he answered, "Say it, Teacher."
41"A certain moneylender had two debtors. One owed five hundred denarii, and the other fifty. 42 When they could not pay, he cancelled the debt of both. Now which of them will love him more?" 43Simon answered, "The one, I suppose, for whom he cancelled the larger debt." And he said to him, "You have judged rightly." 44Then turning toward the woman he said to Simon, "Do you see this woman? I entered your house; you gave me no water for my feet, but she has wet my feet with her tears and wiped them with her hair. 45 You gave me no kiss, but from the time I came in she has not ceased to kiss my feet. 46 You did not anoint my head with oil, but she has anointed my feet with ointment. 47Therefore I tell you, her sins, which are many, are forgiven—for she loved much. But he who is forgiven little, loves little."
48And he said to her, "Your sins are forgiven." 49Then those who were at table with him began to say among themselves, "Who is this, who even forgives sins?" 50And he said to the woman, "Your faith has saved you; go in peace."
Luke 18:9-14 9He also told this parable to some who trusted in themselves that they were righteous, and treated others with contempt: 10"Two men went up into the temple to pray, one a Pharisee and the other a tax collector. 11The Pharisee, standing by himself, prayed thus: 'God, I thank you that I am not like other men, extortioners, unjust, adulterers, or even like this tax collector. 12 I fast twice a week; I give tithes of all that I get.' 13But the tax collector, standing far off, would not even lift up his eyes to heaven, but beat his breast, saying, 'God, be merciful to me, a sinner!' 14I tell you, this man went down to his house justified, rather than the other. For everyone who exalts himself will be humbled, but the one who humbles himself will be exalted."
Luke 23:30-43 39 One of the criminals who were hanged railed at him, saying, "Are you not the Christ? Save yourself and us!" 40But the other rebuked him, saying, "Do you not fear God, since you are under the same sentence of condemnation? 41And we indeed justly, for we are receiving the due reward of our deeds; but this man has done nothing wrong." 42And he said, "Jesus, remember me when you come into your kingdom." 43And he said to him, "Truly, I say to you, today you will be with me in Paradise."
It’s amazing to me that to take positions the Catholics take on some portions of scripture they have to deny or twist other portions of scripture to make it work.