Wrongful dismissal suits are civil suits, not criminal, so the standard of evidence is "the preponderance of the evidence", not "beyond a reasonable doubt". If it's more likely A, rather than B, in the court's eyes, then it's A, even if it still could've been B, I guess, maybe.
So, if you think you were fired because you're gay, you can sue. And your employer will be required to quantify and qualify exactly why you were fired, rather than any other employees. If your job performance is comparable to Bob's, and you had seniority, for instance, why'd they fire you, not Bob?
They don't have to officially state shit. They need to demonstrate there was a valid reason to fire you, specifically, out of all their staff. If it's because you were stealing office supplies or your performance was crap compared to everyone else's, this is an easy thing to prove. If they can't prove it, well, the possibility that it was because of your orientation or identity can absolutely be considered, since you can't show any real cause other than that. And you'll get ruled against, most likely.
Or, in other words, it works exactly like every other protected class legislation that has ever existed, and acting like this is somehow a problem for the courts is completely fuckin' ridiculous.