HID 125khz badge that doesn't respond to 125khz?

There are “crapier” blue cloners that only do EM cards. Your’s might not do HID cards.

Like this one specifically states it does not do HID cards.
https://www.amazon.com/Sdreamland-Handheld-Duplicator-Programmer-Writable/dp/B07JGV9SS7/ref=sr_1_6

So the white cloner is telling you that you scanned an HID card. So the xEM needs to be put in HID mode and then cloned. A cloner will do this automatically based on what kind of card the source card was. When the xEM in HID mode, it will not respond if it is presented to an EM reader and vice versa.

It should be noted that you should absolutely read this FAQ before you attempt to clone your xEM.