For whatever reason, the color is extremely off in Adobe InDesign. I've changed the color settings, restarted my computer, exported to PDF, and nothing is helping. The exported color resembles the very subdued colors in the InDesign display.
InDesign‘s Color Picker is context sensitive—the color or swatch you pick depends on which field your cursor is in. The radio buttons determine the picker’s Color Space View, while the value fields determine the color mode of the chosen swatch or color.
In your .mov your cursor is in one of the C M Y or K fields, so the color you are selecting is CMYK not RGB—note the Add Swatch button is Add CMYK Swatch and not Add RGB Swatch.
InDesign documents don’t have a single color space, there can be a mix of RGB, CMYK, or Lab colors on the same page, so you have to consider the mode of the color you are choosing.
In addition to what's been mentioned already, the question comes down to: What is your intended use of this document? If you are going to print it, you need to think in CMYK terms. In that case, the color picker is doing you a favor in showing that your colors are "out of gamut", i.e. they cannot be printed, so "here's the closest color you can get in CMYK"
Even if you set your workspace to view this document with the bright colours you are choosing, eventually, it will dull down if you send this to print, becasue the printer will have to do that conversion anyway. So, it's best you think/work in your intended output world and stay away from colors you can'r print. This includes a subsection of Pantone spot colors, as they are meant to be printed in specially mixed ink so many of them fall outside the CMYK gamut as well.