If you go into the properties of a single symbol you will see this:
When you activate the layers the symbol is made of, you can set the outline to No color:
However, when you select multiple symbols and enter format symbol(s):
... you will see that the layers button is not available:
You can however, enter the gallery and select the symbol "Circle 1" (which has no border):
which will assign the same symbol to all symbols that were selected:
When you change the color schema it will apply it to the current symbols and you will have no borders:
This was a lot easier in ArcMap and good be enhanced in ArcGIS Pro IMHO.
CC: Kory Kramer