Changing to a different tire size
 

The stock tire size on my 2014 CR-V is 215/70r16. If I replaced all 4 tires with 215/70r16 in the front and 205/70r16 in the rear, would it throw off my speedometer even though my car is front wheel drive and I kept the same diameter in the front? Would there be any issues that would arise from this?

There's a remote chance you could have issues with the ABS system seeing a mis-match between front and rear wheel speeds, but likely it will be fine. I'm fairly certain the speedometer is driven off of 3rd gear in the transmission, so your speedometer will be fine.

Why that combination in tire size?

This is a bad idea. You're making the vehicle more prone to spin outs as the rear is going to be less predictable under severe handling (exactly when you don't want that to happen!)

What were you hoping to accomplish? Better fuel economy? Tire size is a small player compared to the affect make and model of the tire have. So spend your time researching tire brands.

Considering some Asian vans and compact trucks used to have mismatching front and rear wheels, even though they resort to dual rear wheels, I wouldn't be much concerned about such unpredictability.

I put the spare on the back of my leaf and it feels a little twitchy. But that's like a 145mm wide tire.
I don't think you will be able to tell the difference between a 215 on the front and a 205 on the back.

The problem here is that the more unstable tires would be on the rear where what you cited, they are all on the front. Besides, this is an SUV and I'm not sure we want to be making an SUV more unstable.

It's just a 10mm difference, doesn't seem so likely to be too troublesome.

The only situation I recall seeing staggered tire sizes on a FWD car was drag racing Rabbits.

Low wide 13s on the front, and tall narrow 15s on the back. It appeared that matching the contact patch size was the goal.

215/70r16 in the front and 205/[75-80]r16 in the rear?

I have seen a similar approach with other FWD drag-racing cars.