Could back spacing on your rims be causing this issue? Looking at the photos you provided, your wheels seem to sit out a bit.
I have a set of 15's on mine with 215/60 and have no scrubbing of tires. I haven't rolled my fenders either. Measuring from garage floor to highest point of the wheel arch on my car is 26". Next set of tires, I'm entertaining the idea of putting 225's on the rear.

As noted above, you need smaller tires and/or wheels with more backspacing.

If you are looking at getting new 15" wheels anyway, do some measuring and figure out what the backspacing is of your current wheels, how much room you have to add more backspacing and order your new wheels accordingly.

Is your rear wheel 14x7 or 14x8 ?

It looks like there’s an extra inch of “deep dish-ness” on the front side.

205/70-14 tires should not have a rubbing problem at all. My money says that your wheels don't have enough backspace which moves the tire outboard. Correct backspace is extremely critical on the '65/'66 Mustangs because the wheelwells are narrow to begin with. The tire needs to be centered in the wheelwell.

Thanks everyone for the insight! I'll work on collecting more wheel information

HEY NEW GUY....NICE MUSTANG

Hi again! 
Thanks for the welcome! Although I may not be 'new' to the forum, I'm an infrequent poster as I'm relatively young (sub 30) so I enjoy sitting in the back and soaking up all the knowledge you all have accumulated over the years. Since there are almost 9500 posts here, sometimes the answer is hidden in the archives, so I want to be respectful of your time.

I just wanted to post a quick update since I finally had a breakthrough. First, thank you for your insight and suggestions, I was not expecting this to be complicated but I was clearly missing something.

Long story short, it seems that the previous owner decided to put a 1967/68 rear end in the car so the axle is 2" longer than 1965 rear end. This is causing the wheels to sit just outside of the rear fender well causing the rub in the picture. 

I'll also note that I originally led you all astray when I said the tires were 205/70/R14 but they are 215/70/R14, a difference of +.6" which could have caused some confusion. The backspacing is 4.25in, here is a link to the wheel according to the serial number - Magnum 500 - 14x7.

I originally thought that my fix would be to get some combination of wheels/tires that would reduce the overall height of the wheel/tire to stop the rubbing, and rebuild the rear suspension because the old one is worn out. But it seems that project, as they all do, just got a bit bigger than expected.  I also planned on updating the third member to a different gear ratio. 

It seems that I have two options here (in combination with new wheels, tires, rear suspension, and third member): 

1. Get a 1965/66 rear end so that the wheels fit correctly in the wheel wells - I currently have an 8in rear end but I only see 9in rear ends being sold by Currie, Quick Performance, and others. Of course, this requires new spindles, new rear drums (I think), etc. 
2. Keep the 1967/68 rear end, and use the height of the wheels/tires to stop the rub. And see if there is some wheel out there that would accommodate a higher backspace to get the wheel in the fender well. 

I attached a photo so you can see the wheel just outside the fender well. And of the U bolt that I pulled off the rear shock plate which led to this revelation.

(1) https://photos.google.com/photo/AF1QipNYKrRHaS8DDGAB0cEzx6Yona4RtNTWC2pPPTZ6
(2) https://photos.app.goo.gl/8svmssUUtMkHXNyV6

 

Last edited by 65to93 (6/02/2021 4:23 PM)

San Francisco to Castaic is but a mere 350 miles   Seems like a looong haul for sumpin you could probably find on craigslist in Norcal. Mustang MD is the business name, Paul is the owner, and 818-367-0055 is his number.

My 2 cents...............Get wheels with 5" back spacing.  They will bring your wheels in to a perfect fit.  Your axle is  2" wider than a stock '66.  It will work.  I have a spare set of Lincoln MKVII wheels that I install once in a while.  They have 5" bs and fit perfectly with a 1" spacer.