Here is a link to the 4/8/19 episode of Nancy, the critically-acclaimed podcast on WYNC that features stories and conversations about TGBTQ experiences:
In this episode, one of the hosts, Tobin Low, a cisgender gay man, discusses how he came to see me in my office in order to verify if he was lowering his pitch on purpose to avoid sounding too feminine, and whether that was the cause of his vocal fatigue and hoarseness.
The answer was yes. I have seen this quite a bit in my office with a number of clients -- cis or trans, AFAB or AMAB, binary or non-binary, gay or straight -- people who attempt to lower their pitch too much. Typically, it's done for gender identity/expression, to sound more authoritative, to fit in more at work, and/or to avoid homophobia, sexism, and/or transphobia.
If you are trying to lower your pitch, for whatever reason, ask yourself if it sounds hoarse or gravelly, or if your voice gets tired. If so, try to lower your pitch but not quite so low. Try also to keep moving your pitch around in a way that seems like natural English; it doesn't have to be monotone to sound more masculine. If those techniques don't improve your symptoms, consider seeing a behavioral vocal health specialist (speech-language pathologist) to determine if you are going too low or if there is a way to speak at that pitch in a more healthy way.
Later in the podcast, Tobin talks to gender non-binary author and activist Jacob Tobia about embracing their feminine side. Are you embracing your feminine side? masculine side? other side? any side? authentic self? anything that feels right to you? Vocally, anyone can experiment by aiming in whatever direction you want to explore. There is no wrong way to get started as long as you don't push. Your voice shouldn't sound strained or hoarse. Your throat shouldn't hurt or feel vocally tired. Try singing lightly along to a recording in a range that you like, or mimic someone on a video who is talking in a way you like, or just try counting or saying the alphabet in a different way. See what happens. As they say in the podcast, "does it bring you joy"?