You see, a phobia is the fear of something. For example, arachniphobia is the fear of spiders. Claustrophobia is the fear of small spaces. Phobophobia is the fear of dread. Aibohphobia is the fear of words spelled the same way forwards or backward. Hippopotomonstrosesquippedaliophobia is ironically the fear of long words.
The term homo relates to a gay man. The term trans relates to one person switching their gender to the other gender, which is either a male removing their dick and becoming a female, or a female obtaining a dick and therefore becoming a male. Those are the only two genders, mind you, because trans is also just referring to transitioning your gender over to the other, therefore trans is NOT its own gender.
The words homophobic and transphobic have different meanings than what people really say these days. So if we take both of these meanings and put them together, that would mean homophobia is the fear of gay men, and transphobia is the fear of trans people.
So, to answer your question, no, I am not transphobic, because that would mean I am scared when I see a transgender. I just hold a major grudge towards people that switch their entire gender and make it their entire personality, leading to a strong dislike towards them.