It's in the character of Townes that the Netflix series takes the greatest liberties. ... It's important to note that, once again, the show never says that Townes, or even Roger, is gay. We don't get even coded references to Townes' boyfriend, or partner, or traveling companion then, or later.
Is Townes with Roger?
Why Elizabeth & Townes Never Sleep Together
The closest that they come to becoming lovers is in episode 3 “Doubled Pawns”. Beth and Townes run into each other at a chess tournament, years after they first met, and share an intimate moment that's interrupted by the man Townes is living with, Roger.
Did Townes love Beth?
Cleo is the only person who knew that Beth was in love with Townes (or at least that she once was). We never saw Beth speak about her feelings for him with anybody else.