All additional attributes on the public registration form have an ID of "register_{$key}", due the following line in the vanilla theme: (Both on 3.17 as in the 4.*;

File: views/subviews/registration/register_form.twig, line 58

{{ C.Html.textField(registerKey, aSurveyInfo.aAttribute[key],({'id' : "register_{$key}",'class' : 'form-control input-sm'})) }}

but should be:

{{ C.Html.textField(registerKey, aAttribute[key],({'id' : registerKey,'class' : 'form-control input-sm'})) }}

I will create a pull request to fix this later today.