My white flagstone patio wasn't sealed when we moved in and was starting to change colors. Gave it a muriatic acid wash followed by bleach wash and one of them has given half my stone a yellowish color and the other half bright white... Any ideas on where to go from here?

Realistically, it's a natural product so within a few weeks worth of rain/dirt/pollen /dirt/kid's poop/fungus, etc. it will take on a life of its own. I would not try and force it to be any particular shade/tone.

Your limestone patio is going to continue to change color, especially if it is not covered. Pressure washing and use of a bleach mixture will whiten it. Test your pressure washer to make sure you don't pit the stone with high pressure.

You need to bleach the whole thing and lay off the muratic acid which yellowed it. Btw, always test an inconspicuous area first before doing stuff like this.

A sealer will help keep the color from changing somewhat. Apply 3 coats with a pump sprayer spread out over a few days. The limestone will absorb quite a bit. You'll need to re seal at least every other year.

Straight bleach or water it down? I initially did a watered down mixture. I'm trying to get it as close to uniform as I can before I seal it.

Even diluted acid may stain it. I agree with the least intrusive pressure washer nozzle. Get a good rough surface and seal it then.

If you don't dilute the bleach it will erode the limestone.