Let's say it was your standard brick n mortar retail store. This employee would have to face customers.
Let's say the applicant is good, well qualified and apparently reliable.
As a manager/boss, you ultimately have the final say. Let's say this transgender was a... very "obvious" transgender.
You have to balance both sides, morality/ethics vs customer experience.
Let us respect people's opinions, and just because someone says no, let us not assume they are transphobic or phobic-anything.
For example, there are some roles which favour females (e.g. receptionists) and it doesn't mean the manager is misandrist, just that the manager wants a female facing their clientel.
Me? I probably wouldn't, at least not in a job where you face customers daily. We've all been in that situation where we are with someone random, and the only thought in our head is "is that a boy or girl? :o"
That's not really the reaction you want consumers to have. When you see a transgender, you often think immediately "this is a trans-person" even if you completely are accepting of their lifestyle. It's just that thought though and you feel like they would be more of a liability, even if they are completely hard working.
Your answer? be brutally honest and I do not mind if you tell me I am wrong.