You absolutely can. If you think your dismissal was due to a discriminatory reason, you can absolutely challenge it, no matter what was actually officially given as the reason. After all no one ever writes "fired for being black" yet people win racial discrimination cases all the time. 2 years or not, you have that right.

What you cannot do is challege as dismissal as unfair for any non-discriminatory reason. It has absolutely nothing to do with what the employer wrote down as the reason for dismissal, it's the question of what grounds are you challenging them on.

Yeah, but then you have to prove it. Previously your employer had to show the dismissal was fair, now you have to show it was not. In such subjective cases, that is very hard. Like you say, no one will say "you're too black, you're fired". But before they had to actually have a reason that wasn't subjective. Now they don't, they can hide behind the equivalent of "no comment" and you have to find evidence...