Though now considered a linchpin of conservative politics, the speech was originally intended to disseminate socially and economically liberal ideals.

Here's an analysis of the sentence and the correct answers for the blank:
1) Explanation

Let's break down the sentence to understand the context and the meaning required for the blank:
- "Though now considered a linchpin of conservative politics, the speech was originally intended to $\qquad$ socially and economically liberal ideals."
- "Though now considered a linchpin of conservative politics": The word "Though" sets up a strong contrast. A "linchpin" is a crucial element. So, the speech is currently seen as central to conservative politics.
- "originally intended to $\qquad$ socially and economically liberal ideals": Because of the "Though" contrast, the original intention must have been the opposite of supporting conservative ideals, meaning it was meant to promote or spread liberal ideals.

Therefore, the blank needs words that mean to promote, spread, or make widely known.

Let's evaluate the given options:
- A. crystallize: To make something definite or clear. While a speech might clarify ideals, "crystallize" doesn't primarily mean to spread or promote them.
- B. disseminate: To spread or disperse (something, especially information) widely. This perfectly fits the idea of spreading liberal ideals.
- C. obscure: To make unclear or difficult to understand; to conceal. This is the opposite of what's needed.
- D. promulgate: To promote or make widely known (an idea or cause). This is a strong synonym for "disseminate" and also perfectly fits the idea of spreading liberal ideals.
- E. castigate: To reprimand (someone) severely. This is irrelevant and the opposite of promoting.
- F. placate: To make (someone) less angry or hostile. This is irrelevant.

Conclusion:

The context clearly indicates that the speech's original purpose was to spread or promote liberal ideals, contrasting with its later perception. Both "disseminate" and "promulgate" accurately convey this meaning.

The final answer is $\(\mathrm{B}, \mathrm{D}\)$.