Since MySites uses the Loggedin user to figure out what MySite to access
I don't see how they would work after enabling  Anonymous Access. I
assume what you really want is to Enable Anyone to access  The Public
view of a Mysite. To do that I would try setting up
NTAuthority/Authenticated users with a Read Policy to the MySites
WebApplication Policy.

You are correct. I have a public facing web  site and would like to use
MySite functionality to server as personal pages  for staff people and
show them to the outside world. Thanks for the idea. I tried it and it
didn't work. Why would giving authenticated users read access  to the
site help non-authenticated users view the public version of the profile?

Any other thoughts?

I thought it might work because anonymous  users are automatically
authenticated as IUSR_computername. I know it doesn't work on regular
sites, but thought it might on MySites. Anyway, you can turn on
Anonymous access  in Central Administration on the Operations panel in
Authentication Providers. Then go into site  Settings for a MySite and
turn on Anonymous access from the Settings menu of Advanced Security.

The problem is that since each MySite is a Site Collection you will have
to set  it on each individual MySite. Some of these settings can be
defaulted prior to creating the MySite by navigating manually to the
_Layouts/Settings.aspx page of the root of the MySite provider and
setting things there. But I tried that and it doesn't look like
Anonymous Access is propogated to the other MySites when they are
provisioned like some of the settings.

You could probably write a WEB scoped Feature to modify the
AnonymousState property of the SPWeb, then staple the Feature to the
MySite template and set it to autoactivate. Then when the site is
provisioned the Anonymous Access capability would be enabled.

Question - and forgive me if this reveals my relative newness to SharePoint
- would it also work to extend a web  application to allow those profiles to
be viewable, or am I misunderstanding the use of that functionality?

You can extend a Web Application to provide a specific URL for anonymous  Access
externally. The problem is that you still need to specify what anonymous users
can access  at the Site Collection level and each MySite is its own Site
Collection. Extending the Web App would just provide me a different Zone URL so
that I could have one URL with anonymous possible and another without.

Here is what I have done so far.

1) Created a web  application policy giving NT AUTHORITY\authenticated
users full read access.
2) Made sure that anonymous  access was turned  on for the My site  web
application.
3) Made sure that anonymous access  was turned on in the site
collection where the person.aspx page was.
4) Used feature stapling to set  AnonymousState to on.

Still I am being required to authenticate when I try to hit
....mydomain.com/.../Person.aspx\dcp

It seems strange to me that you can't easily enable  anonymous access.

Ok, #1 & #4 are not needed if you do #2 & #3 manually. However, when
you say that you turned  Anonymyous access  on for the site  collection
where person.aspx is I assume you mean mysites.mydomain.com/mysites/
Site collection. The problem is that when you access the URL you listed
it redirects you to http://mysites.mydomain.com/mysites/dcp/
<http://mysites.mydomain.com/mysites/dcp/> Site collection. Anonymous
Access needs to be turned on there as well. Have DCP go into the
SiteSettings->Advanced Security->Settings menu to see if Anonymous
access is turned on for their Site Collection.

#4 was an attempt to Automate turning on Anonymous Access when the
MySite was created. This requires #2 to be already completed and will
only work for new sites created AFTER you do the Feature stapling.

I don't think Microsoft ever envisioned anyone having external
Non-authenticated users who could access the personal information on
MySites. By default, anyone who is authenticated(whether they have an
account in SharePoint or not) has Read access to MySites.

I'm having the same issues with enabling  anonymous access  on "My
Sites."

I wonder if anyone has an idea of why I can't get it to work.

I've done (or I think that I have) everything (outside of stapling)
that's been recommended in this thread, but I just can't seem to get
it working for "My Sites." Here is a summary of what I'm trying to
do, and what I have done.

Any and all feedback is greatly appreciated!