NJT and Metro-North/LIRR let anyone buy senior fare tickets on the app. I guess the conductor has the right to ask for ID when you show the ticket. They've never asked me, but my hair is nice and grey.
I have a NYC senior MetroCard for the subway and buses. I had to provide a passport photo and send a notarized copy of my Maryland driver's license, as I ordered it by mail. I'm not sure if I've yet saved the cost of the photo, notary, and UPS shipping of the application.
Before the pandemic, I used to be able to buy a senior light rail ticket in Baltimore from the ticket machine. Again, the tickets are checked onboard, and I suppose the inspector can ask for more ID, if needed. On the Baltimore Metro, they don't have senior tickets in the vending machines, but the attendant will give you one on payment of the fare. MARC requires you to register for senior fares, which requires an online application that includes your driver's license or state ID number. Not clear whether they accept out of state ID. I can now buy all the senior MARC tickets I want on the app. When I was working, I got a senior monthly pass when I turned 65, but I forget what I had to do to get it. The real hassle was changing my transit subsidy, which involved coordinating WMATA (my Senior SmartTrip card), MARC, the local Agency that handled the transit subsidy (Commer Direct? or Commuter choice?), and the Federal Agency I worked for. Getting the Senior SmartTrip card involved a trip to the sales office at the Metro Center station (which fortunately was only a block from my office), and showing them my driver's license. My Maryland license was, of course, no problems, so I don't know what their policy is on Senior cards for people living outside of MD, DC, or VA.
I haven't bothered to get a senior card for Boston or Chicago. The Boston one would involve another trip to the Charlie Card store at the Downtown Crossing Station. The Chicago one looked like it had so much red tape that it wasn't worth the bother for a place that I might only visit once every 2 years or so.
I started using Amtrak senior fares when I turned 62. Then they jacked up the minimum age when I was 63 or 64, so I had to go back to regular fares until I turned 65.