Hi there - also a newbie here.
I've come across exactly the same effect with my new X-T20; it's almost as though the image is printed on a fine canvas. I've eventually traced it to my RAW conversion process. I'm still using Photoshop CS6 as I don't like Adobe's Creative Cloud 'Rental only' payment system, so the X-T20 isn't recognised and I had to use Adobe's DNG converter to download usable DNG files. When I opened the converted files in CS6 I had exactly the same pattern as you.
After reading a few forums I've now downloaded Iridient X-transformer (for Mac or Windows) which is specifically designed for the X-Trans sensor and the problem is gone. The cost is under £30 and it's slow but brilliant for X-Tran sensor files and gives you usable DNG files you can edit in your usual software.
I hope this helps.
Phil