Absolutely. Everyone should have the same rights independent of how they identify themselves.

That being said, except for extremely rare cases (as in something around 1:1,000,000) every human has one biological sex. Claiming that you are the opposite sex of your biological birth does make a difference that I understand for a lot of people, particularly women who have had to fight since the dawn of time to get even close to the same rights as men.

My wife, for example, took extreme umbridge that recently international woman's day was represented in an international ad campaign (here in central Europe) by two trans women. Not to put to fine a point on it, these two people do NOT know what it is like to grow up as a woman, because they didn't. Have a trans-Woman's day then, OK? Let biological women have their day for themselves. It is not like they've had it for 100 years. Hell, my mom had to have my dad sign off so she could have a credit card.

Let's recognize that biological sex and sexual identity are two related but different categorizations. Neither should be used to discriminate, but they are NOT interchangeable.

If you go to the hospital for an infection, you're going to be treated on the basis of your biological sex, not your sexual identity - or you might have serious health problems as a result of the wrong treatment.

I think we should enjoy the differences we have rather than trying to force everyone to pretend they don't exist. That won't work. If you're born a man but want to be called Andrea rather than Andreas, fine by me. If you want to fight my daughter in MMA as Andrea after going through male puberty, NOT fine by me.