I did a little more digging and have a solution that should benefit others.
The problem:
Form Helper does not properly display URLs or email addresses when “Automatically turn URLs and email addresses into links?” in Admin > Weblog Management > Weblog Posting Preferences is set to Yes.
The solution:
Set “Automatically turn URLs and email addresses into links?” to No.
Install the Auto Linker plugin.
Install the HTML Strip plugin.
In your template, add the Auto Linker tags to the website address that needs to be hyperlinked like this:
{exp:auto_linker}{website}{/exp:auto_linker}
For whatever reason, the email address ignores the Auto Linker tag so you have to hard code the email address and use HTML Strip in your template like this:
<a href="mailto:{exp:html_strip}{email_address}{/exp:html_strip}">{email_address}</a>
In your template, set the email address and website fields to display as textareas. It does not seem to matter if the custom field in EE is set to Text Input or Textarea. Just be sure the template sets the field to be a textarea. The template code will look something like this:
<textarea name="{exp:form_helper:field_grabber field_name="email_address"}" cols="60" rows="1" />
{exp:form_helper:field_parser}{email_address}{/exp:form_helper:field_parser}</textarea>
And that’s it.
Some drawbacks:
Users can add more than one email or web address to the textarea.
It doesn’t look as nice as a Text Input box.
The mailto link is hanging out there just waiting for spammers to grab it.
Hope that helps others avoid some grief.