No it is not ok to not hire someone because they are straight or white.
HOWEVER, saying that, when you have to make a choice between two equal people, all that's left is, the people themselves as a deciding factor.
We're not talking about someone protected by "Equal Opportunity" so your hang up on that is irrelevant in this case. There is no law forcing them to hire the transgender person. Simply put, they can look up, be uncomfortable and say no. Considering being transgender creates that reaction almost everywhere, because simply put, employers don't want to deal with that in their work place. It can potentially create issues with not only them, but other workers being uncomfortable. There's no reason for them to hire the transgender person, it's an annoying hassle. So when I say hiring the transgender person is the right and good choice in that scenario, it's because it is, because chances are, no one is going to hire them because they don't have to, and because there is no incentive for them to buck the norm. It's potential an HR nightmare, they can avoid by simply saying no.
I'm not talking about a, not hiring the straight white over the transgender because of some forced "Equal Opportunity" law. I'm talking about taking an active effort to make a difference, despite it being more convenient to do like everyone else and just tell the Transgender to go away.
See the issue is that when a Transgender applies for a job, and the straight white guy applies for a job and both are equally skilled, without any protection there is no incentive to hire the transgender, none what so ever. In fact even if the Transgender is more qualified, the issues that come with hiring a transgender person is quite likely enough that they will say no anyway to avoid such issues.
This creates a situation where it's damn near impossible to get hired as transgendered in any job. This is why there are so many transgendered prostitutes, and is why I personally find the transgender prostitute so common in tv shows and movies so offensive. Because those that are, often end up such out of desperation because no one will hire them.
Is your father completely unhireable? Do you feel there's an honest chance he'll have to turn to crime in order to support his family? Because that is reality for someone Transgendered unless they get lucky or live in a place more progressive towards LGBT rights.
Now how do you THINK we should handle this? As current the only way a Transgender gets justice in these scenarios is long drawn out legal fights we usually lose, putting us in an even worse position, with the occasional victory far rarer than the loses.
See you don't seem to get the difference between your father and the other scenario. Your father may not have gotten the job he wanted, but he got a job. If nothing was or never is done to force the issue, it'd be just your father and people like him getting jobs. A lot of people would be perfectly happy if transgendered starved and died, because we make them feel a little uncomfortable and they don't want that in their work place.
Does the occasional straight white guy get boned by efforts to force the issue? Yes of course they do. And that sucks and is wrong, but no where near as wrong as the situation that happens far more often and flagrantly on the other side, for which doing nothing means no progress, ever.
Now that being said, after enough time has passed when there is no longer a stigma on hiring a certain group of people, such laws need to be relaxed, and if full acceptance occurs, possibly eliminated completely, or becoming a law that merely defends against not hiring someone based on such issues period including straight white. But when it is so lopsided that the only way one side is not starving and selling themselves on the street is with help and luck, and the straight white guy is in no danger of not finding a job anywhere, then I admit to having difficulty feeling bad they didn't get their dream job, when the other side is struggling to get any job, dream/hated/or otherwise.