Do I have to cut my hair by regulation AR-670-1 if I’m retired?

While you are no longer subject to Army regulations, it would be a common courtesy for you to at least come close to the standards if you intend on wearing the uniform. Showing up looking completely unsat would not bring credit on the uniform, the service, or you.
If you are proud of the uniform, wear it right.
Afterthought - if you were going to show in civvies or the RWB t-shirt or something, you could come looking like ZZ Top and nobody would say a word to you.

If you are going to wear it then yes you should cut your hair accordingly... but the guidelines are pretty generous as far as hair length.... the problem
Is if you grew out a sick beard.

It doesn't have to be STARC or high& tight, but if wearing a uniform be neat and close the regs.

It will grow back

If you are planning on wearing a uniform, I would suggest you look tidy.

Long hair and a nasty beard. If you want to wear it according to military standards then do so. You are free to do whatever you want now.

Stuff it under your hat ... that's what we did in the old days.

If you wear the uniform, you have to adhere to 670-1/DA PAM, including shaving.

If you wear a uniform of a VSO, that is that organization's standards.

AR 670-1 para 21-3
"(b) Wear the uniform in accordance with the guidance provided to AA Soldiers in DA Pam 670–1."

No regulation

Of course not!!!!!!