Answer: Let's break it down by each question:
Why would a single state's judge be able to make this kind of call for an agency such as the FDA?
There are both federal courts and state courts. State courts, as you can probably guess, deal with matters of state law. Federal courts, as you can also probably guess, deal with matters of federal (nationwide law).
Because the US is so big, it's divided into 13 "circuits" (as seen on this map). Within those circuits, there are further subdivisions, often along state boundaries, but also within states (especially for big states like Texas). This particular case is a federal one. However, the starting point just happens to be in the Northern District of Texas. If the case gets appealed, it will advance from the district to the 5th Circuit (region that includes Texas, Louisiana, & Mississippi). If the case gets appealed again, it goes up to the highest federal court, the Supreme Court.
In other words, this is a federal case based on federal law. It just happens to be taking place in northern Texas with a judge from that physically works there.
And what does Washington's block mean in regard to what the Texas judge is doing?
Just like a federal case can begin in Texas, another federal case could begin in a different location as well. It just so happens that a case in the State of Washington dealt with a very similar topic but with the judge making the opposite ruling. Judges in different districts are all equal, so a higher level court (i.e. the Supreme Court) is going to need to figure out whose ruling makes the most sense legally.
What would the Supreme Court be deciding here if it goes up to them and what would the FDA be required to do if our right leaning Supreme Court sides with Texas?
The Supreme Court would need to evaluate the contradictory rulings and determine the ultimate status of mifepristone. They could decide that one judge's ruling overrules the other or that elements of each ruling are both correct. In short, they could determine that the drug is legal for doctors to prescribe, illegal for doctors to prescribe, or only legal in a limited set of circumstances. If they side with Texas, the drug falls into the illegal category.
