Judas: An Instrument Chosen to Carry Out God's Plan

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Someone posted in a Reformed Christian Facebook group that the verse, "You did not choose me, but I chose you" was only referring to Jesus choosing His disciples and pointed out that He chose Judas as a disciple.

Yes, Jesus chose Judas as one of His disciples but not for the reason of salvation. We read in Psalm 41:9: "Even my close friend in whom I trusted, who ate my bread, has lifted his heel against me." This verse, even though spoken by David, is a prophecy of Christ being betrayed by a friend. David is known as a foreshadow of Christ and this verse, along with Psalm 22, is a prophesy concerning Christ's betrayal and crucifixion. You can also read other verses in the Old Testament that prophesies about Judas' betrayal here. Jesus chose Judas to fulfill prophesy. Remember what Romans 9:17 says: "For the Scripture says to Pharoah, 'For this very purpose I have raised you up, that I might show my power in your, and that my name might be proclaimed in all the earth.'"
God chose Pharoah for specific purpose and that was to show His power in him. Remember after the first several plagues that occurred, it said that Pharoah hardened his heart? After that, Scripture says that God hardened his heart. That was the power of God working in Pharoah's heart. God had a purpose for Pharoah and "raised" him up for that purpose which was to release the Hebrews from their yoke of slavery in Egypt. Then God had Pharoah killed along with his army (Psalm 136:13-15) when God brought the waters of the Red Sea back together after the Hebrews crossed over. In His prayer in John 17, we see in verse 12 Jesus praying: "While I was with them, I kept them in your name, which you have given me. I have guarded them, and not one of them has been lost except the son of perdition, that the Scripture might be fulfilled." Judas was not one of those whom God had given to Jesus for the purpose of salvation. He was not guarded as the other disciples were because Scripture had to be fulfilled. Jesus called him the "son of perdition". The term perdition means "eternal damnation" or "utter destruction". You can read more about this here. Someone who is considered a "son of perdition" is one who is in an unredeemable state and the term shows there is no forgiveness planned for them. They are doomed to destruction.
God can use anyone to carry out His decreed will. Judas was chosen, as one who was already condemned, to carry out the betrayal of Jesus for the purpose of fulfilling Scripture. Same with Pharoah. God raised him up for the purpose of freeing His chosen people to go into the Promised Land and then God destroyed him. So, yes, Jesus chose Judas, but the purpose of choosing him wasn't for salvation. It was for the purpose of fulfilling Scripture.