Selective Service
I called the Selective Service and this is what I believe from them.
If you were/are residing in the US between the ages 18 & 26 then you have to check their web site to see under which criteria you could be excluded from registering. For eg, if after I485, you were in parole status and no longer have H1-B Visa, and you are/were still under 26, and if you had not registered, then you may face problems in the future like citizenship being denied which could also lead to re-entry denial into US if you stayed out of US too long.
I was specifically told then when applying for citizenship or any benefits, I would have to provide documentary proof that I was not required to register.
A green card holder who is under 26 must register.