VSCode – Is there a way to customise double-click select behaviour?

Since this issue has been resolved it’s worth adding this answer.

You can now accomplish this in your settings by modifiying the "editor.wordSeparators" setting.

Here is the default:

"editor.wordSeparators": "`~!@#$%^&*()-=+[{]}\\|;:'\",.<>/?"

To allow the selection of $foo you can remove the $ from the above string.