Не работает echoMode() для QLineEdit в PyQt5

Попробуйте так:

import sys
from PyQt5 import QtCore, QtGui, QtWidgets


class MainWindow(QtWidgets.QMainWindow):
    def __init__(self):
        super().__init__()
        self.initUI()

    def initUI(self):
        self.setFixedSize(700, 440)
        self.setWindowFlags(QtCore.Qt.FramelessWindowHint)
        self.setFocus()

        self.centralWidget = QtWidgets.QWidget()
        self.setCentralWidget(self.centralWidget)

        self.fon = QtWidgets.QLabel(self)
        self.fon.setPixmap(QtGui.QPixmap('images/fon.png'))
        self.fon.resize(700, 440)

        self.logo = QtWidgets.QLabel(self)
        self.logo.setPixmap(QtGui.QPixmap('images/logo.png'))
        self.logo.resize(46, 46)
        self.logo.move(40, 30)

        self.login_label = QtWidgets.QLabel(self)
        self.login_label.setStyleSheet('''
        QLabel {
        border-image: url(images/text.png);
        }
        QLabel:hover {
        border-image: url(images/light_text.png);
        }''')
        self.login_label.resize(383, 42)
        self.login_label.move(40, 120)
# +++
        self.login_input = QtWidgets.QLineEdit(
            self, placeholderText=self.tr("Email or username"))
            
        # снятие фокуса с login_input
        self.login_input.setFrame(False)
        self.login_input.setStyleSheet('''
        QLineEdit {
        background-color: rgba(0, 0, 0, 0);
        color: blue;                                   /* <---- white */
        }''')
        self.login_input.resize(363, 15)
        self.login_input.move(50, 135)
        self.login_input.setFont(QtGui.QFont("Arial", 11))

        self.reg_label = QtWidgets.QLabel(self)
        self.reg_label.setStyleSheet('''
        QLabel {
        border-image: url(images/text.png);
        }
        QLabel:hover {
        border-image: url(images/light_text.png);
        }''')
        self.reg_label.resize(383, 42)
        self.reg_label.move(40, 196)
# +++
        self.reg_input = QtWidgets.QLineEdit(self,
            placeholderText=self.tr("Password"), 
            echoMode=QtWidgets.QLineEdit.Password
        )
        self.reg_input.setFrame(False)
        self.reg_input.setStyleSheet('''
        QLineEdit {
        background-color: rgba(0, 0, 0, 0);
        color: blue;                                   /* <---- white */
        }''')
        self.reg_input.resize(363, 15)
        self.reg_input.move(50, 211)
        self.reg_input.setFont(QtGui.QFont("Arial", 11))
        
#        self.reg_input.echoMode()                         # не работает

        self.exit_button = QtWidgets.QPushButton(self)
        self.exit_button.setStyleSheet('''
        QPushButton {
        border-image: url(images/exit1.png);
        }
        QPushButton:hover {
        border-image: url(images/exit2.png);
        }''')
        self.exit_button.resize(32, 32)
        self.exit_button.move(668, 0)
        self.exit_button.clicked.connect(exit)


if __name__ == '__main__':
    app = QtWidgets.QApplication(sys.argv)
    w = MainWindow()
    w.show()
    sys.exit(app.exec_())