Varnish first.  That way you have a smooth uninterupted surface to varnish. Just easier. 

My opinion only.

Ed

The impression I get after reading the instructions is that as long as the eye straps are glued directly to epoxy (not to varnish) either way is fine. If there is varnish there, remove it before bonding. When applying future coats of varnish, the eye straps can also receive a coat. It doesn't say whether the eye straps themselves need a UV protective coating.

I would certainly check with CLC before relying on them for great strength. Even then I would be leery about using them to hang the kayak from, or to tie it to a vehicle. That might just be me ...

Old Yeller

If you are referring to the CF padeyes, I have used them.  They are really cool looking, and in my opinion, look much better than using webbing screwed to the deck, forming and eye.  I epoxyed them before varnish, you need a good bond, and I felt that trying to remove varnish to get a clean surface was counter productive.  It is a bit of a hassle to varnish around, left little imperfections underneath the padeye, but the bungee cord hides it.  I didn't varnish over them, I liked the clean look.

I have used them on several kayak builds... I use them on the bungee tie downs.  I was a little concerned for using them for lifelines or lifting my kayaks.

I installed them after varnishing.  Either way you will still need to scuff up the mating with 220 grit sandpaper for adhesion.  If you follow the CLC instructions with cutting out the attaching surface via blue tape.  Make sure you pull out the center tape under the loop before you affix the CF.

Thanks all, great tips.

my intent with these is to have a bow tie for use at my lake when it'll be easier to leave it for short periods in the water.

Ill put another at the stern for the leash and 4 up front for bungee storage. Not going to use for hanging or tie downs.   

The site does say they are incredibly strong though.