Can a Retiree with a shaving profile wear the ASU or AGSU with a beard?

If you're retired, you don't have a no shaving profile anymore. You're not on active duty...once you left active duty any profile you had issued from a provider won't apply anymore. Neither would the religious exemption.

This is what 670-1 has for the paragraph on retired personnel:

23–3. Retired personnel
a. Personnel who will be advanced to a higher grade upon retirement have the option of wearing the insignia of that grade thereafter.
b. Retired personnel on active duty will wear their uniform and insignia in the same manner as prescribed for personnel in the RA of corresponding grade and branch.
c. Retired personnel not on active duty may wear either the uniform reflecting their grade and branch on the date of their retirement, or the uniform prescribed for personnel in the RA of corresponding grade and branch, when appropriate, but may not mix the two uniforms. Personnel will wear the grade as shown on the retired grade of rank line on their retirement order.
d. Retired personnel not on active duty are not authorized to wear the Army uniform when they are instructors or responsible for military discipline at an educational institution, unless the educational institution is conducting courses of instruction approved by the Armed Forces.
e. In addition to the occasions for wear listed above, retired personnel are authorized to wear the uniform only on the following occasions:
(1) While attending military funerals, memorial services, weddings, inaugurals, and other occasions of ceremony.
(2) Attending parades on national or state holidays, or other patriotic parades or ceremonies in which any Regular or Reserve U.S. military unit is taking part. Uniforms for these occasions are restricted to service and dress uniforms; the combat uniform and physical fitness uniforms will not be worn. Wearing the Army uniform at any other time, or for any other purpose than stated above, is prohibited.
f. Retirees are authorized to wear the physical fitness uniform under the following provisions:
(1) With civilian attire off the installation.
(2) When wearing the physical fitness uniform as a complete uniform, retirees will—
(a) Wear only authorized accessories corresponding to those worn by personnel of the RA.
(b) Wear the uniform in accordance with the guidance provided to RA Soldiers (see DA Pam 670–1).
g. Retirees are authorized to wear the Retired Service Identification Badge (see DA Pam 670–1).
h. Retirees are authorized to wear the Retired SSI (see DA Pam 670–1).

It says only "retired personnel on active duty" wear the unfiorm and insignia in the same manner as personnel on RA.

But you can only wear it in the instances listed...I bet if you have a neatly trimmed beard no one would care if they know you're retired. I honestly don't know why anyone would wear their uniforms after they retire but that's on them. I'm putting all my military stuff away when I retire.

I just don’t get the desire to keep wearing the uniform after retirement. To me uniforms are for the ones still in. To each his/ her/ it’s own.

If you are retired you don't have a shaving profile or no shaving chit because you aren't in any longer. Anything you had while in has since expired because you left.

With that said, the expectation is to wear the uniform correctly and to look good in uniform according to policy. Will it make people mad to see someone in uniform with a beard regardless of anything else? Yes. Will veterans or retirees end up doing what they want anyways? Yes.

If somebody gets lifed out for having a beard in uniform and pulls out an ancient profile from a million years ago they will be laughed at directly in their face