footnote superscript number in text always has unchangeable gray background

edit

To complement @RGB-es's answer, you can set the colour to any you like in Tools>Options, LibreOffice>Application Colors, Text Document section, Field Shadings item. The check box there is an alias for the one at View>Field Shadings.

I strongly recommend against disabling this shading because it indicates something managed by LO Writer and not by you. If you disable the shading, you end up with no "reminder" of special properties and you could erase it without any warning (visual clue) about the consequence, i.e. the simultaneous deletion of the associated note.

You can change the colour, but the chosen gray is relatively non-obtrusive.

That grey background is there only during edition to tell the reader that that is just a field: that background does not get printed or exported to PDF so you don't need to worry about it. In fact, if you go to "print preview" it's not shown. You can always disable that background with View → Field shadings.