Here’s another alternative way.

There’s no direct way to influence the color selection chip on the Data Validation itself what you can do instead is use on Edit and just change the background after selecting.

Depending on your end result this could be a helpful work around.

You can try this code using Google App script:

function applyDropdownColor() {
  var sheet = SpreadsheetApp.getActiveSpreadsheet().getSheetByName('Sheet1');
  var sourceRange = sheet.getRange('A1:A20');
  var backgrounds = sourceRange.getBackgrounds();

  sheet.getRange('B1').setDataValidation(
    SpreadsheetApp.newDataValidation()
      .requireValueInRange(sourceRange, true)
      .build()
  );

  var firstValue = sourceRange.getValues()[0][0];
  if (firstValue) {
    sheet.getRange('B1').setBackground(backgrounds[0][0]);
  }
}

function onEdit(e) {
  updateBackgroundColor(e);
}

function updateBackgroundColor(e) {
  var sheet = e.source.getActiveSheet();
  var targetCell = sheet.getRange('B1');

  if (e.range.getA1Notation() === targetCell.getA1Notation()) {
    var selectedValue = e.value;
    var sourceRange = sheet.getRange('A1:A20');
    var values = sourceRange.getValues();
    var backgrounds = sourceRange.getBackgrounds();

    values.forEach((row, i) => {
      if (row[0] === selectedValue) {
        targetCell.setBackground(backgrounds[i][0]);
      }
    });
  }
}

This script creates a drop-down menu in cell B1 that lets you choose from A1
and changes B1’s background color based on your selection.

The updateBackgroundColor function ensures that when you pick a value from the drop-down, B1’s background color updates match the color in A1.

Sample Output:

Reference/s:

getBackground

onEdit

I can’t seem to find a way to do that dynamically (that is, for the colours of the options to change automatically if the reference cells’ background colours change) in Apps Script.

However, if the background colours of your reference range are meant to stay fixed, you can manually format the colour of the drop-down options in the Google Sheets ‘Data validation rules’ side menu:

Use the colorfulDropdownLists_ script.

For best effect, choose the Arrow display style instead of the Chip display style in dropdown Advanced options.