How to implement radiobuttons field on frontend registration form?
Because radio inputs are a "single value field", meaning that when the form submits, only one value actually goes through, you don't need the extra [] array brackets at the end of each fields[] array.  In fact, you don't even need the hidden field above it.  That setup would work for checkboxes, where any number of values could be submitted. A great reference for how to format HTML form fields correctly to submit to Craft can be found on this StraightUpCraft article.

Your code should look like this:

&lt;label&gt;
    &lt;input type="radio" value="yes" name="fields[areYouBeekeeper]" {%- if account is defined %}value="{{ account.areYouBeekeeper }}"{% endif -%}&gt;Yes
&lt;/label&gt;
&lt;label&gt;
    &lt;input type="radio" value="no" name="fields[areYouBeekeeper]" {%- if account is defined %}value="{{ account.areYouBeekeeper }}"{% endif -%}&gt;No
&lt;/label&gt;


And the input values yes and no need to be exactly the same (lowercase in this case) as they are in the Values column of the respective custom radio field created in the CMS.