The arrival_time column is displayed, so that probably means the error isn’t actually in the rendering. Most likely, the issue has to do with your filtering.
If you run your code through the debugger in RStudio, you can see that this line of your code:
stop_times.kept[stop_times.kept$stop_id %in% input$Stop,]
produces 0 cases, which is why your table looks empty. I think you set up the subsetting wrong here (you have set it to look for matches for stop_id, which is an integer, but the user input from input$Stop are the stop names, which are characters). If you fix this, the table output should be fixed!
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