This is in Unity/Desktop build
This is on WebGL
There is a small black “scanline” between rows of tiles.
I have to amend my initial bug report. It seems the bug appears also on desktop. It appears and disappears depending on the camera position.
I fixed it by using a RenderTexture with a low resolution. Looks much better that way. 
Are the tiles in a sprite sheet or separate images?
All in one single sheet.
Do you have an buffer or borders around the tiles?
I had the same problem, a thin black line at the edges, but with hex tilemaps, and it was blurry. The solution was to set the “Filter Mode” in the texture setting of each tile image to “Point (no filter)” (default was “Bilinear”), now the thin “scanlines” are gone.
BTW, I didn’t found a documentation how a hexagonal tilemap has to look like to be displayed seamless. Of course, there are not many ways to to it pixel perfect, maybe only one. Anyway, below is an (zoomed) example for a 64x64 tile that I use. The two pixels at the top and the bottom aligns perfectly and seamless to the one pixel at the top left, top right and bottom left, bottom right side (two of it) when placed.
