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Context rules.
For reference...

John 13:2 DURING supper, when the devil had already put it into the heart of Judas Iscariot, Simon’s son, to betray him.

Matthew 26:21And AS they were eating, he said, “Truly, I say to you, one of you will betray me.

Luke 222:21 But behold, the hand of him who betrays me is with me ON the table.

John 13:27ff THEN after he had taken the morsel, Satan entered into him (JUDAS). Jesus said to him, “What you are going to do, do QUICKLY.”
28Now no one AT THE table knew why he said this to him.
29Some thought that, because Judas had the moneybag, Jesus was telling him, “Buy what we need for the feast,” or that he should give something to the poor.
30So, AFTER receiving the morsel of bread, he (JUDAS) IMMEDIATELY went out. And it was night.

John 13:3ff Jesus, knowing that the Father had given all things into his hands, and that he had come from God and was going back to God,
4rose FROM (AFTER) supper.(JUDAS IS GONE) He laid aside his outer garments, and taking a towel, tied it around his waist.
5Then he poured water into a basin and began to wash the disciples’ feet

Washing of the disciples feet happened after Jesus LEFT THE TABLE and after He dipped the bread. This is when when Judas ran out. Jesus was at the table when Judas ran out. The foot washing happened after Jesus left (rose from) the table.

The WHOLE counsel of God tells the whole timeline, not narrowly selected verses.

NOWHERE in Scripture does Jesus wash the feet of sinners.

Submitted respectfully as correction to false teaching.

For further edification, we’re told WHY Jesus washed the disciple’s feet, later in John 13:17. This is critical to understanding the actions of Jesus.

6He came to Simon Peter, who said to him, “Lord, do you wash my feet?”
7Jesus answered him, “What I am doing you do not understand now, but afterward you will understand.”
8Peter said to him, “You shall never wash my feet.” Jesus answered him, “If I do not wash you, you have no share with me.” (Judas has already left the scene yet not betrayed Jesus.)

Judas had no “share with [Jesus]”!

14If I then, your Lord and Teacher, have washed your (the disciples) feet, you also ought to wash one another’s (disciples) feet.
15For I have given you AN EXAMPLE, that you also should do just as I have done to you.

The “who” in this passage is paramount. Who is Jesus a addressing?
His disciples!

And how did Jesus define a disciple of His?
Luke 9:23Then he said to them all: “Whoever wants to be my disciple must deny themselves and take up their cross daily and follow me.”

This absolutely didn’t describe Judas.
Jesus didn’t wash the feet of Judas.