Once selected my radio buttons can't be deselected in a stand alone PDF. Please advise how to fix it?

I created a fillable form in LibreOffice Writer. I then create a PDF and everything works well except when I accidentally select the wrong button, I try deselecting it and it can’t deselect.

Are you talking of an Option Button? If so, why do you call it “radio button”?
Option buttons are designed to be used in groups where finally exactly one of many (at least tow to make sense) shall be selected.
For “on/off” , “selected/unselected”, "checked/unchecked, “enabled/disabled” Check Box controls are made.
A rather strict terminology is very useful in forums and Q&A sites.to make answers “re-findable”.
Different software may prefer a different name for a functionally equivalent thing. In the given case “Option Button (aka radio button)” might be an option to get it unambiguous.

Cool down. Although “radio button” is somewhat 80ish, it’s a recognized term for a multiple selection list where only one choice CAN and MUST be selected. You’ll need to find your dad’s old stereo to understand.
Unselection is not possible and would belong in the “Interface Hall of Shame”.
http://hallofshame.gp.co.at/shame.htm

I’m completely cool, I know, and I used “radio buttons” sometimes when programming with visual components. They also were grouped and**…**
It’s simply not the term used in LibO.
[In the later 1950es I actually used a Radio having a key field where pressing one key released the previously pressed one (mechanically). Actually that “SABA” device also had an OFF key which leleased itself (had no pawl). That’s the functionalty, but the view was completely different. Recent hardware also often has similar functionality, may it be a radio or somethging else.]
You will sulrely invent “radio buttons” in groups allowing the selection of up to three options. Long needed.

It’s Bug 127217.

The question is about UNselecting a button. The bug you refer to is about not being able to select a button. Not the same issue, I think.
Radio buttons can’t “unselected”. The only thing you can do is select a different button.

Actually you can un-set an Option Button - use a macro:

  oDrawPage = ThisComponent.getDrawPage()
  oForms = oDrawPage.getForms()
  oObj1 = oForms.getByName("Form")
  
  oObj2 = oObj1.getByName("Option Button 1")
  oObj2.State = 0

I do agree that option buttons are not meant for this purpose but it can be done. It, however, is not of help in a PDF form since macros are not available through LO.

The intuitive operation of an option button (aka “radio button”) list would be to have one field active as default when starting.

There is nothing intuitive about it. Just like buttons on an old radio, I can have all not selected. Then, of course, there is the on/off button. Opens a whole new avenue.