You can consider the Hidden in Filter option, for a filter field. So in essence, for your portlet's filter field, modify the Active field, to have the Hidden in Filter option check marked, along with the default option.
In which case, when you click on the Clear button, the fields defaulted filter option would be retained, for example, Active would still remain as check marked and accordingly the portlet's output would be displayed.
Hence, even if the Clear button is present, it would still retain the hidden filter option.
Disabling out of box buttons is generally not recommended, you may refer to the attached document, which discusses the above points, step by step.
Hope this helps you.
Regards,
Samik