I want to add a new cell to the top of the table view without causing the current position to be pushed down. Note that I'm also not removing the cell I would like to add to the top, but rather just also adding it to the top.

ios-tableview-add.swift

import UIKit

class ViewController: UIViewController, UITableViewDataSource, UITableViewDelegate {
    let tableView = UITableView(frame: CGRect.zero, style: .plain)

    var totalAdded = 0
    
    override func viewDidLoad() {
        super.viewDidLoad()
     
        tableView.translatesAutoresizingMaskIntoConstraints = false
        tableView.register(UITableViewCell.self, forCellReuseIdentifier: "MyCell")
        tableView.dataSource = self
        tableView.delegate = self
        
        view.addSubview(tableView)
        
        view.addConstraint(NSLayoutConstraint(item: tableView, attribute: .top, relatedBy: .equal, toItem: view, attribute: .top, multiplier: 1.0, constant: 0.0))
        view.addConstraint(NSLayoutConstraint(item: tableView, attribute: .bottom, relatedBy: .equal, toItem: view, attribute: .bottom, multiplier: 1.0, constant: 0.0))
        view.addConstraint(NSLayoutConstraint(item: tableView, attribute: .left, relatedBy: .equal, toItem: view, attribute: .left, multiplier: 1.0, constant: 0.0))
        view.addConstraint(NSLayoutConstraint(item: tableView, attribute: .right, relatedBy: .equal, toItem: view, attribute: .right, multiplier: 1.0, constant: 0.0))
    }
    
    func numberOfSections(in tableView: UITableView) -> Int {
        return UILocalizedIndexedCollation.current().sectionTitles.count + 1
    }
    
    func tableView(_ tableView: UITableView, numberOfRowsInSection section: Int) -> Int {
        return section == 0 ? totalAdded : 8
    }
    
    func tableView(_ tableView: UITableView, cellForRowAt indexPath: IndexPath) -> UITableViewCell {
        let cell = tableView.dequeueReusableCell(withIdentifier: "MyCell", for: indexPath)
        cell.textLabel?.text = "Oranges \(indexPath.row)"
        cell.accessoryView = createStarAccessoryButton()
        return cell
    }
    
    func sectionIndexTitles(for tableView: UITableView) -> [String]? {
        return ["*"] + UILocalizedIndexedCollation.current().sectionTitles
    }
    
    func tableView(_ tableView: UITableView, titleForHeaderInSection section: Int) -> String? {
        return section == 0 ? "Favorites" : UILocalizedIndexedCollation.current().sectionTitles[section - 1]
    }
    
    func createStarAccessoryButton() -> UIButton {
        let button = UIButton(type: .system)
        button.tintColor = .lightGray
        button.setImage(UIImage(systemName: "star.fill")!, for: .normal)
        button.sizeToFit()
        button.addTarget(self, action: #selector(starButtonTapped(sender:)), for: .touchUpInside)
        return button
    }
    
    @objc func starButtonTapped(sender: UIButton) {
        let buttonPosition = sender.convert(CGPoint.zero, to: tableView)
        guard let indexPath = tableView.indexPathForRow(at: buttonPosition) else { return }
        let height = tableView.cellForRow(at: indexPath)!.bounds.height
        
        let oldContentOffset = tableView.contentOffset.y
        
        totalAdded += 1
        tableView.reloadData()
        
        // The ol' "dispatch ahead one run loop iteration" sorta works most of the time :/
        DispatchQueue.main.async {
            self.tableView.contentOffset.y = oldContentOffset + height
        }
    }
}

Solution per Nathan Lawrence, don't use reloadData just use the cell insert methods! Doh!

@objc func starButtonTapped(sender: UIButton) {
    let buttonPosition = sender.convert(CGPoint.zero, to: tableView)
    guard let indexPath = tableView.indexPathForRow(at: buttonPosition) else { return }
    let height = tableView.cellForRow(at: indexPath)!.bounds.height
    
    let oldContentOffset = tableView.contentOffset.y
    
    totalAdded += 1
    
    tableView.performBatchUpdates {
        self.tableView.insertRows(at: [IndexPath(row: 0, section: 0)], with: .none)
    } completion: { (didComplete) in
        self.tableView.contentOffset.y = oldContentOffset + height
    }
}

Oh gosh I didn't realize how much I butchered the indentation in the main gist. I'm so sorry!