How to create a login page in shiny?

Here is my solution. It is not perfect but it is simple.

library(shiny)

ui <- fluidPage(
        conditionalPanel(
          condition = "input.password != 'password'",  
          textInput("password", "Password:", value = "Type the password here")
        ), 
        conditionalPanel(
          condition = "input.password == 'password'",  
          fluidRow(
               column(2,
                 textInput("Green", "Green:", value = "24716"), 
                 textInput("Blue", "Blue:", value = "24700")
               )
          )
        ),  
        plotOutput(outputId = "distPlot")
)

server <- function(input, output, session) {
  output$distPlot <- renderPlot({
    if (input$password!="password") return(0)
    plot(c(1,2,3),c(1,2,3))
  })
}

app=shinyApp(ui, server)

I think you have two issues here:

First your confirm button value is stored here: input$"ui1Output-confirm" and not here: input$confirm

I would suggest to replace:

observeEvent(is.null(input$confirm), {
  Logged <<- F
})

By:

observeEvent(input$"ui1Output-confirm", {
    Logged <<- T
})

Then your observe function does not contain any reference to the button so it is not executed when the user clicks on it. I don't have a proper solution for this but a simple hack would be to add:

tmp <- input$"ui1Output-confirm"

at the begining of the observe section:

observe({
    tmp <- input$"ui1Output-confirm"

    if (Logged == FALSE) {
        output$page <- renderUI({ 
            ui1Output('ui1Output') 
        })
        output$lsuId <- renderText({ input$lsuId })
    }
    if (Logged == TRUE) 
    {
         output$page <- renderUI({ ui2 })
    }
})