Custom designed ships listed under Specialty ships

It is tied to what modules you are using. Check that you're not using any speciality items that would come under that.

I selected a battleship hull from the hull templates and then outfitted it with three enhanced railguns, promethium drive, advanced shield generator, advanced point defense, 2x hull plating, foundry and a slipstream accelerator.  It does have the battleship icon right beside it in the list. So, I iteratively removed one module after another until there was just one railgun on it. Still no luck. So, I went and started from scratch, same hull, just one railgun on it. Same result. So, I thought maybe I am doing something wrong and just went to design from scratch, without cosmetic pieces, I grabbed one of these Slyne sphere models and put a railgun on it, same result. 

This is caused by the Auto Favorite feature.  I believe it is on by default.

There is no section for favorite ships, so they go into the Specialty Ships section.  I just verified it by making a military ship with Auto Favorite on.  It went into the Specialty Ships section.  Turn off Auto Favorite to prevent that in the future.

The ships you made can be removed from that section by selecting the ship and clicking on the star at the bottom of the screen.

Thanks! That was exactly it. Once I turned auto-favor off and removed it from the favorite list, it got fixed.