No, it's not transphobic. People have a right to date or not date others based on their personal preferences. Transphobic would be more along the lines of hating, fearing, etc. transgendered people because they are transgendered. To equate transphobia with someone's preference in who to date is incredible.
Like almost everyone above the age of 13, I've been rejected as a date from time to time. Sometimes the rejection has upset me. But I've never thought that anyone who rejected me was therefore a misandrist, heterophobic, or otherwise displaying anything but a legitimate personal preference.