It's a complicated issue. When it comes to bathrooms it's easy to say, use the bathroom that aligns with the sex you were assigned at birth... but what if you're a fully transitioned and expressing male to female transgender woman that passes 100% as a woman? Would you want that person to use the men's bathroom?
Sports is another issue, and again it's complicated. Everyone wants fairness in sports. I would say sports by their very nature are unfair. People are born with certain biological advantages over other people..height, strength, speed, intelligence. Of course there's tons of training involved but the person with the best training AND the biological advantages will usually come out ahead. Then if you throw performance enhancing drugs into the mix that also skews everything. Maybe they can make the rules that in order to participate in women's sports as a transgender woman you have to be fully transitioned for a certain number of years and have the testosterone levels and estrogen levels of an average woman. But that doesn't take away the advantage of the male frame. So yes it doesn't seem fair if a male athlete, so someone who already probably is above average in a lot of biological qualities that make them good at sports...transitions well into adulthood, and then competes with women in sports like powerlifting, swimming or MMA where they can dominate.
Do we limit the type of sports transgender women can compete in? Make separate leagues for transgender athletes? I don't have a good answer but I think we should at least try to find a solution that doesn't make female athletes feel like the game is rigged but also doesn't make transgender athletes feel excluded or marginalized.