To maintain the viability of certain industries, the plan outlined by the junior senator from Missouri required that new government legislation
should allow drilling for fossil fuels in national forests, should reduce restrictions on pollution levels, and should establish a new oversight committee dedicated to enforcing these changes.
In Subjunctive mood- Subject + Bossy word (command/demand/suggestion/necessity/dictate/mandate) + that + basic form of verb.
"required" jumps out for me, It is a bossy word. So, we need a basic form of verb.
A) should allow drilling for fossil fuels in national forests, should reduce restrictions on pollution levels, and should establish a new oversight committee dedicated to enforcing these changes -> "should" is not required in subjunctive mood construction. Incorrect.
B) should allow drilling for fossil fuels in national forests, reductions of restrictions on pollution, and establishing a new oversight committee -> Same error as A and there is parallelism error too. It is easy to eliminate. Incorrect.
C) should allow drilling for fossil fuels in national forests, reduce restrictions on pollution, and establish a new oversight committee -> It is similar to A and doesn't follow subjunctive mood construction. Incorrect.
D) allow drilling for fossil fuels in national forests, reduce restrictions on pollution levels, and establish a new oversight committee -> Now, we have subjunctive mood construction followed. Now, we see "and", so, Let's check parallelism. "allow...", "reduce..." and "establish..." are parallel to each other. Let's keep it.
E) allow drilling for fossil fuels in national forests, reduce restrictions on pollution levels, and establishment of a new oversight committee -> Again, we have subjunctive mood construction followed. But, "establishment" is a noun, it is not parallel to "allow" and "reduce". Incorrect.
So, I think D.