Well said. If the person is completely unqualified for the job, then it would be fine not to give them the job. It's just that this doesn't happen. Transgendered people are often given very menial jobs for no reason other than being transgendered. What they are capable of doing is ignored.
And this is a truly deplorable situation.

I think an employer has every right to run his/her business as they see fit for the business.

True, but surely there ought to be means of protecting people with no power against an employer who enjoys picking on people. I don't want to be fired for something as trivial as being ginger, so if I am I can claim "unfair dismissal".

Employers aren't the only people with rights.

Not entirely no, quite a lot of private business relies on public infrastructure and society needs to work together as a whole, it's part of the social contract. Leaving businesses to discriminate as they please could lead to the establishment of quite a few ghettos.

I suppose then, that an employer should be entitled to pay their employees $1.50/hour if they so decide to cut costs in their business? Especially in these hard economic times where many people will accept a job at such a meager pay level. It's hard for businesses to stay afloat. Surely it's justified?

And exactly what you are saying is why an employer might dismiss someone such as a transgender, from peer pressure. As long as the public infrastructure does not accept this, then businesses have no choice but to either cater to them or fail.

We change the cultural point of view first and then we'll see everything else change accordingly. Bottom line in business is to stay in business, if you cater to a client that abhors green men, you tend to avoid hiring green men, if a purple man changes his color to green it will be jeopardizing the business and a decision needs to be met.

Personally I wouldn't want to work somewhere knowing that I was only employed because the employer was mandated to do so. I imagine it would be a very difficult position to be in. On the one hand if you don't assert yourself then nothing is going to change but if you do it doesn't make for a comfortable work environment.

Well, isn't that against the law?

But it's the logic behind it. It's saying that there are aspects about workers rights that aren't under the control of the owner.

Abercrombie and Fitch/Banana Republic are actually guilty, and have had successful lawsuits taken against them, of racial discrimination. The company caters to skinny, blonde, white customers, and as such has discriminated against qualified individuals of differing ethnicities, either choosing not to hire them, or keeping them in the warehouse and out of site. Is this acceptable, and why?