Seasoned DIY painter here.
The real estate agent knows what helps a house sell, and that includes being able to imagine their own furnishing and possessions in a house. Your color choices are perfect for you, I assume, but their boldness will make potential buyers unable to envision the house as their own.
So yeah, listen to the realtor. A pale neutral like grey, cream, or white lets anybody see themselves in the house. My own recommendation on color would be to use a light ash grey only in a warm climate, since it will appear cool. Use cream in a cool climate, since it looks warm. White is fine in either, but kind of boring.
And bear in mind that you need your paint color to coordinate with carpet, tile, window treatments, etc. even if they're not all staying. The house has to look good with what buyers will see. You don't paint cream when you have white blinds, like we did on our first house. (We repainted.)
Use flat paint on walls and be prepared to do two coats, three if the color is radically different. (Maybe prime that burgundy wall?) Use a satin or semi-gloss on window and door frames, and other trim. Usually you use white for trim. Do not paint trims that are now bare wood unless you do it to cover damage.
Since this paint job isn't for your own tastes, buy one color of wall paint and one of trim in quantities to do the entire house. Two adults without kids underfoot can paint a coat a day in one room, maybe two if they prepped the night before.