_______________ to her superstitions, the mumpsimus irrationally avoided black cats.

The correct answer is clinging.

Step 1: Understand the sentence structure and vocabulary
The sentence reads: "_______________ to her superstitions, the mumpsimus irrationally avoided black cats."
A "mumpsimus" refers to a person who obstinately adheres to or holds onto unreasonable customs, beliefs, or errors despite being shown that they are wrong.

Step 2: Analyze the options in context
We need a participle that correctly pairs with the preposition "to" and fits the context of holding fast to superstitions:

1. clinging: "Clinging to" means holding tightly to a belief, idea, or habit. This fits logically with "superstitions" and the behavior of a "mumpsimus."
2. falling: "Falling to" does not fit the context of adhering to superstitions.
3. loosening: "Loosening" would mean releasing or weakening a grip on superstitions, which contradicts "irrationally avoided black cats."
4. dropping: "Dropping" means abandoning, which also contradicts the irrational avoidance of black cats.

Step 3: Conclusion
"Clinging" is the only option that correctly completes the phrase "clinging to her superstitions," describing someone who steadfastly holds onto superstitious beliefs.