To me, Burnham in her mess hall scene represented the Federation's world and moral compass all turning to shit so nobody wanted to sit with her for fear of being infected by her perceived toxic perspective. They all believed in the Federation and its principles and, at this early stage in the war, may have been terrified to examine those core beliefs too deeply or even risk having them questioned.
Tyler's mess hall scene, in contrast, occurs at a time when the Federation's ethics and procedures (even though distorted by Terran Lorca) have seen the crew through a particularly trying and dangerous time and so the crew sit with him because they fear losing the Federation principles which have served them so well and are, after all, what they've been fighting to preserve.
I see basically the same fear driving both scenes and resulting in different outcomes based only on time and circumstance. The fear of losing the Federation's principles, to my mind, explains both scenes without any need whatsoever to bring sex, race, creed or colour into the mix.