Monogame v3.6(3.5 too). I'm using this tutorial from this page: gamedevelopment.tutsplus.[dotcom]/tutorials/make-a-neon-vector-shooter-in-xna-bloom-and-black-holes--gamedev-9877 with shader model ps_4_0_level_9_1 in DirectX context. In OpenGL project all working fine. I've already checked my solution and empty solution with bloom with simple sprite render, both directx. Both have problems. Screenshot: https://postimg.org/image/7c47ckt1j/
Intel Core i5 4200 with integrated graphics.
I'll try this https://github.com/UncleThomy/BloomFilter-for-Monogame-and-XNA but I think this problem is interesting.