How to replace fluidRow with a horizontally scrollable non-wrapping row in tab panel?

How about using a carousel instead e.g. via shinyglide or slickR:

library(dplyr)
library(DT)
library(shiny)
library(shinyWidgets)
library(shinyglide)

ui <- 
  fluidPage(
    titlePanel("Summary"),
    sidebarLayout(
      sidebarPanel(
        selectInput("selectData", h5("Select data to view:"),
                    choices = list("Beta"),
                    selected = "Beta"),
      ),
      mainPanel(
        tabsetPanel(
          tabPanel("Private data", value = 1,
                   conditionalPanel(condition = "input.selectData == 'Beta'",
                                    fluidRow(div(style = "margin-top:15px"),
                                             column(12, glide(
                                               height = "25",
                                               controls_position = "top",
                                               screen(
                                                 p(strong("Group 1")),
                                                 wellPanel(    
                                                   radioButtons(inputId = 'group1',
                                                                label = NULL,
                                                                choiceNames = c('By period','By MOA'), 
                                                                choiceValues = c('Period','MOA'),
                                                                selected = 'Period',
                                                                inline = TRUE
                                                   ),
                                                   style = "padding-top: 12px; padding-bottom: 0px;"
                                                 )
                                               ),
                                               screen(
                                                 p(strong("Group 2")),
                                                 wellPanel(    
                                                   radioButtons(inputId = 'group2',
                                                                label = NULL,
                                                                choiceNames = c('Exclude CT','Include CT'), 
                                                                choiceValues = c('Exclude','Include'),
                                                                selected = 'Exclude',
                                                                inline = TRUE
                                                   ),
                                                   style = "padding-top: 12px; padding-bottom: 0px;"
                                                 )
                                               )
                                             ))
                                    ),
                                    DTOutput("plants")
                   )
          ), 
          id = "tabselected"  
        ) 
      ) 
    ) 
  ) 

server <- function(input, output, session) {
  output$plants <- renderDT({iris %>% datatable(rownames = FALSE)})
}

shinyApp(ui, server)