Sometimes it won't let you set the icon. I mean it show a normal quick map dialog, I click an "set an icon" button, and it does nothing.
But, if I create an tag with name (complete the dialog), and then re-open standard "edit tag" dialog — i can set an icon without issues.

Looks like I have this issue with blinking marker from the Big-monsters mod https://mods.factorio.com/mod/Big-Monsters
(a random event, with cross marker on the map).
If I try add the quick tag over this blinking marker — sometimes it blocks an icon setting.

I don't think there's a mod conflict here, maybe you can reproduce this behavior if you re-create the flashing marker in your test code - just add a marker and remove it once a second.