No, I support personal privacy.
You asked about Scriptural Support for Personal Privacy and I examined multiple translations in a word search for "privacy". I was able to locate only one translation that used the English word 'privacy' in any scripture verse (the NLT) and that was the only verse that any translator felt the word privacy was included in the equivalent thought translation. It appears in no equivalent word translation.
I cannot claim that the Bible says something that it does not.
Do you have any verses you feel address the question of personal privacy?
Absent any other verses, I have answered your 'theological' question about what scripture says to the best of my ability.
God empowered a prophet to violate the personal privacy of an evil King by providing secrets to a foreign King. That is God empowered government violation of personal privacy.
Here's a selection of verses using "private"
(Genesis 43:32) Joseph was served at his private table, the brothers off by themselves and the Egyptians off by themselves (Egyptians won't eat at the same table with Hebrews; it's repulsive to them).
(Numbers 25:8) and followed them into the tent. With one thrust he drove the spear through the two of them, the man of Israel and the woman, right through their private parts. That stopped the plague from continuing among the People of Israel.
(Judges 3:19) But when he got as far as the stone images near Gilgal, he went back and said, "I have a private message for you, O king." The king told his servants, "Leave." They all left.
(Judges 17:5) This man, Micah, had a private chapel. He had made an ephod and some teraphim-idols and had ordained one of his sons to be his priest.
(Judges 18:31) All during the time that there was a sanctuary of God in Shiloh, they kept for their private use the god-figure that Micah had made.
(2 Samuel 3:19) Abner took the Benjaminites aside and spoke to them. Then he went to Hebron for a private talk with David, telling him everything that Israel in general and Benjamin in particular were planning to do.
(2 Samuel 19:5) But in private Joab rebuked the king: "Now you've done it--knocked the wind out of your loyal servants who have just saved your life, to say nothing of the lives of your sons and daughters, wives and concubines.
(2 Samuel 22:7) A hostile world! I called to GOD, to my God I cried out. From his palace he heard me call; my cry brought me right into his presence-- a private audience!
(2 Kings 7:9) Finally they said to one another, "We shouldn't be doing this! This is a day of good news and we're making it into a private party! If we wait around until morning we'll get caught and punished. Come on! Let's go tell the news to the king's palace!"
(2 Kings 11:2) But Jehosheba, daughter of King Joram and sister of Ahaziah, took Ahaziah's son Joash and kidnapped him from among the king's sons slated for slaughter. She hid him and his nurse in a private room away from Athaliah. He didn't get killed.
(2 Kings 15:25) And then his military aide Pekah son of Remaliah conspired against him--killed him in cold blood while he was in his private quarters in the royal palace in Samaria. He also killed Argob and Arieh. Fifty Gadites were in on the conspiracy with him. After the murder he became the next king.
(2 Kings 18:24) You can't do it? Well, then, how do you think you're going to turn back even one raw buck private from my master's troops? How long are you going to hold on to that figment of your imagination, these hoped-for Egyptian chariots and horses?
(2 Kings 18:27) But the Rabshakeh said, "We weren't sent with a private message to your master and you; this is public--a message to everyone within earshot. After all, they're involved in this as well as you; if you don't come to terms, they'll be eating their own turds and drinking their own pee right along with you."
(2 Kings 23:8) He swept the outlying towns of Judah clean of priests and smashed the sex-and-religion shrines where they worked their trade from one end of the country to the other--all the way from Geba to Beersheba. He smashed the sex-and-religion shrine that had been set up just to the left of the city gate for the private use of Joshua, the city mayor.
(2 Chronicles 22:11) Jehosheba, daughter of King Jehoram, took Ahaziah's son Joash, and kidnapped him from among the king's sons slated for slaughter. She hid him and his nurse in a private room away from Athaliah. So Jehosheba, daughter of King Jehoram and Ahaziah's sister--she was also the wife of Jehoiada the priest--saved Joash from the murderous Queen Athaliah.
(Esther 5:12) "On top of all that," Haman continued, "Queen Esther invited me to a private dinner she gave for the king, just the three of us. And she's invited me to another one tomorrow.
(Psalms 18:6) A hostile world! I call to GOD, I cry to God to help me. From his palace he hears my call; my cry brings me right into his presence-- a private audience!
(Song of Solomon 4:12) Dear lover and friend, you're a secret garden, a private and pure fountain.
(Isaiah 14:11) This is where your pomp and fine music led you, Babylon, to your underworld private chambers, A king-size mattress of maggots for repose and a quilt of crawling worms for warmth.
(Luke 10:23) He then turned in a private aside to his disciples. "Fortunate the eyes that see what you're seeing!
(Luke 12:3) You can't whisper one thing in private and preach the opposite in public; the day's coming when those whispers will be repeated all over town.
(Acts 28:16) When we actually entered Rome, they let Paul live in his own private quarters with a soldier who had been assigned to guard him.
(1 Corinthians 14:2) If you praise him in the private language of tongues, God understands you but no one else does, for you are sharing intimacies just between you and him.
(1 Corinthians 14:4) The one who prays using a private "prayer language" certainly gets a lot out of it, but proclaiming God's truth to the church in its common language brings the whole church into growth and strength.
(1 Corinthians 14:13) So, when you pray in your private prayer language, don't hoard the experience for yourself. Pray for the insight and ability to bring others into that intimacy.
(1 Corinthians 14:16) If you give a blessing using your private prayer language, which no one else understands, how can some outsider who has just shown up and has no idea what's going on know when to say "Amen"?
(Galatians 2:2) I went to clarify with them what had been revealed to me. At that time I placed before them exactly what I was preaching to the non-Jews. I did this in private with the leaders, those held in esteem by the church, so that our concern would not become a controversial public issue, marred by ethnic tensions, exposing my years of work to denigration and endangering my present ministry.
(2 Peter 1:20) The main thing to keep in mind here is that no prophecy of Scripture is a matter of private opinion.