You are sure hung up on the world "real" let me tell you that to me you are not a real woman or human because you lack the necessary component of one - empathy. Your whole communication style is there to slash and draw as much pain as possible from the safety of your screen. My assesment of you as human sludge dweller is just as valid or non valid as you categorisation of "real" there are factual arguments supporting my claim but is it really the whole picture?
While it is your right to hold your opinion, the way you chose to do it is cruel and you are making sure to take no prisoners! No one is arguing that trans people are biologically the sex they express yet it becomes your sole narrative. Fact is, that which you have admitted to knowing, that most trans women/men show brain chemistry opposite to that of their biological sex. Fact is being born in the wrong body is a birth defect and correcting this birth defect comes with a lifetime of dangers and sacrifices. Taking hormones has dangers, losing you ability to have biological children is a huge sacrifice. Trans people are well aware that they will never be biologically whole there is no need to plant neon signs around them and your version of the westboro baptist church in every stroke of your keyboard! No you choose these things because it makes you feel better about your poor self but to anyone with a "real" heart it just makes you vile beyond stomaching! Would you run after someone who is blind and make fun of their lack of vision? Would you make sure to point out someone born with no arms that they have no arms again and again? No you would not because the world would not let you get away with it ! But here by pure arbitrary luck you are biologically whole and it seems that you have little else to build your self esteem on; so you feel the need to bully and harass those who were not so lucky to have at least something to brag about.
Tell me in your world would anyone who is born intersex have to make sure to label themselves not "real" as well ? Or a person who had reconstructive surgery should they make sure to tell the world they had a defect that was fixed? Why in your opinion should a trans person wear a scarlet letter for all to see ? To make sure the partner knows they are not fertile? Does this mean that a biological female that is not fertile or has a hysterectomy should wear the T-shirt to make sure the world knows this ? And if not what is the difference here?
And now to the point of experience, I do not know about your education level but it seems to me that you might be lacking in that department. You are aware that no two humans experience their reality in the very same manner right? This is backed by psychology, sociology and science! You filter your world and your experiences through the unique lense of culture, family dynamics, individual biology and personal experiences. No two women experience this planet or life in the exact same way as you do and cultural norms vary so even the cultural expression of a"real" woman changes depending on location and who you are with. It is simple your freedom ends at another's skin and your right to express your views does not give you a freepass to be a douche. Sure you can categorise people into your boxes if it makes your poor self feel safer but you will also have to deal with people putting you in their own little ugly boxes ...