Often times the lower hen feather will contact the shelf if you are shooting cock feather out. Although it may seem counter intuitive, try shooting cock feather in. If the arrow is properly tuned to the bow, the cock feather will not contact the shelf due to the paradox the arrow experiences as it leaves the bow.
But how do you even know it's hitting? Did you video it? If the outer part of the feather is hitting, it should not be a problem because the feather bends easily. Isn't that why we use feathers instead of vanes off the shelf? However, if the shaft itself could hit at the base of the feather, wouldn't that mean that the string nock is a little too low?
Feathers are forgiving, but they are not supposed to hit the shelf each time you shoot, or they will show premature wearing. The contact is likely caused by one or both of the following problems.
1) As StevenB suggests, your string nock may be too low. The arrow is launched too close to your rest or shelf and makes contact.
2) Your arrow is too stiff. It does not bend enough to give adequate clearance as archer's paradox allows the shaft to pass around the riser and causes the lower hen feather to strike the shelf.
Shooting cock feather in, as J-san describes, is a method to cope with a marginally low nock point or stiff shaft.
At some point you will want to bareshaft tune your bow to make sure your nock point is set correctly and your arrow's spine is matched to your bow. There is more than one way of doing this. I think the method on Morrison Archery is fairly simple.
It is about 10 mm too high - I have used bareshaft test to find the optimum nocking point height.
See this (from side):
You can see, how the arrow is going up - too much.
By the way, I am shooting self made bamboo backed bow, no shelf. If nocking point is too low, arrow is hitting my hand. More convenient to shoot, if the nocking point is just right. Of course, the accuracy is a big bonus...!