Ok, I did some tests... all on 1080p. Random Gen. And I of course re-loaded the world for each test and allowed the fps to settle.
Reflections set to high next to large body of water with sun reflecting off of it: 105fps
Reflections set to off next to large body of water in the same position: 115fps
Reflections set to high inside a house looking at a reflective stove among other kitchen stuff: 56fps
Reflections set to off inside the house in the same position: 60fps
"Reflected shadows" setting didn't seem to make any difference with shadow distance set to near, maybe 1 or 2fps difference?
Shadow distance set to Far next to large body of water (same position), with trees / foliage covering half the screen: 99fps
Shadow distance set to off next to large body of water and trees / foliage: 107fps
Shadow distance set to Far inside the house in the kitchen: 57fps
Shadow distance set to off inside the house in the same position: 68fps
Shadow distance set to Near inside the house in the same position: 60fps
Conclusion, I think reflections don't impact performance enough to stand out from any other graphics settings. The only reason there was a 10fps difference with the water was because the the sun reflects a lot off of the water, so when it's disabled, the water just becomes a flat color. So of course reflections would have a pretty big impact on that. Also, the world looks kind of bad without reflections, so I think it's worth turning down other settings just to have it on.
I wanted to do more tests, but the time of day seems to impact the fps results by over 20fps difference. So I did what I could within daytime.