Ok, transphobe here
Though i do not like trans people that much and i don't believe in "trans christians", i don't really think shoving down opinions to people's throat will solve the problem, that will just turn them against your own beliefs and may turn even more cynical.
Your older brother is definitely in the wrong here, cause we all know that in the verse of Matthew 7:1-2, the bible says "Do not judge, or you too will be judged, For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you"