This does not bother me too much because I intend on removing the theme switcher and locking in the light theme but I noticed that my site on mobile when switched only switches the drop-down menu.
Steps to reproduce the behavior:

@shariq1989 Thank you for reporting the issue. I couldn't fully reproduce the bug, but noticed a slightly different glitch. When I click on the text/icon on FF it would switch, but not if I click besides it (on the blank space around). Is that the same for you or does it not switch at all?
It won't switch if clicked beside, only when the icon is clicked. And it only ever switches the drop-down menu. The issue I brought up is only happening on my mobile browser FF, nowhere else. Working fine in mobile Chrome as well.
It seems like it is moreso the dark mode on my phone that was forcing the issue. Once I turned that off, the site started functioning as expected.