So I believe that we all have the right to identify however we choose
Op, what do you mean by "identify as"? As I understand it this usually means "I say I am, even though I'm actually not"
regardless of our gender at birth.
How are you defining "gender at birth"? Are you using gender to mean sex? By saying "at birth" you imply it can be different at other points during the person's life -is that how you mean it?
But I also think that women have the right to be safe and due to the risk to women that men pose I feel women do need safe spaces and also their own space in sports otherwise they risk losing their identity in sport.
For the most prt I heartily agree, but only if by "women" you mean adult female humans and by "men" you mean adult male humans. I don't think it's our identity in sport that we will lose though, it's our spot on the team, on the podium and in the changing room.
So to me the answer is womens spaces, gender neutral spaces and mens spaces. Gender neutral encompasses male, female, trans male, trans female, gender neutral, pan gender, non binary etc.
As others have said here and on the duplicate posts, many women have suggested this and been shut down because for those wanting in to female spaces (the people who shouldn't be there) it's not actually about safety. It's about being in spaces designated for women and how good that makes them feel. If we had third spaces, those people wouldn't use them, they want to be in with us. If we then all decided to use the empty third spaces, they might then follow. And we'd be at square one, sharing spaces with people who aren't women.
The way I see it is we live in an inclusive society
Depends what you mean by "inclusive". We live in a society that tries its hardest to be inclusive of non-women in women's sapces because that's what some non-women want. Those spaces then become exclusive of women with trauma, fear of male violence and those who follow orthodox religions.
that recognises peoples right to live their life as they choose
If the people doing the choosing are male and the choice is to enter female spaces
but the need for women safety is paramount.
Women's safey isn't paramount though, and that's why we've ended up in this mess.