Yes so it is an issue with Mozilla Firefox which you will need to investigate yourself.
If it all works fine in all other browsers than it can’t be a code issue and therefore this Wix Corvid Forum can’t help you as it can’t provide you with code that would work specifically on Mozilla Firefox only and not on Microsoft Edge or Google Chrome or Apple Safari etc.
What you might find happening is that Mozilla Firefox is only seeing the dropdown element itself and is not including the actual dropdown list as part of the element, so when you move the mouse away from the dropdown element the onMouseOut event handler function will kick in and it will blur, or do whatever else you have setup on it.
The issue on your Mozilla Firefox site is that the onMouseOut event handler function is probably only working on the dropdown menu itself, once you move the mouse away from the dropdown element it will go off.
You would be better off using a seperate container that appears when the user clicks on an arrow icon so that you can use onMouseout on that container too and not just the dropdown element itself.