I love working on outdoor spaces!! Starting with painting the fence and walls white will give you a nice blank space to work with.
Instead of trying to combat the green of the furniture, try to find ways to incorporate it into the design! Green is, after all, the most commonly found color in nature, and you know my obsession with decorating with plants. You could put up a trellis with some bougainvillea or another vine-heavy plant (like roses!) for a more feminine, garden-esque vibe, or put some outdoor plants like cacti or succulents in plant stands (like I did for Joslyn!) and have those be a key design element!
Adding a nice outdoor carpet could be a good way to hide the brown of the floor if you don’t love it, or to bring in a more neutral or colorful (your decision!) vibe into the space. Also think about adding an outdoor stool, or some new, unique piece of furniture into the mix. It’s all about layering, so the green of the furniture doesn’t look like something you have to design around or overcome, but part of the plan initially!