Sam and Mendral are not attracted sexually, no.
But two things are going on here. One...Sam in the canon universe (in "Lower Decks") sometimes seemed a bit awkward and likely to beat up on himself. (Remember that awful, awkward conversation with Riker?) Two...he's suddenly met someone who will not look down on him for his beliefs and I think that he's as much overcome by what that means spiritually, as he is by the in-the-moment awkardness.
The way I imagine them as the friendship forms, they're like brothers, these two--close enough to be family in all but blood. And I think they ARE concerned about letting other people see it, exactly because of how it can be misinterpreted.
You are right that Mendral learned to write with pen and paper, not on the computer. He's not trying to look pretentious...he does this to connect with his past and the traditions he grew up in.
And yes, in this case--what you are seeing of Federation society and the intolerance is how I see both the canon and AU versions of the Federation.