What does “Commander-in-Soy” versus “alpha” mean?

The usage is Commander-in-Soy, which is a play on words on the president's role as Commander-in-Chief of the U.S. Armed Forces. Note that Soy is capitalized in this usage.

One soy product is actually called "commander":

It means that Trump displayed weak, "feminine" characteristics by backing down on his pledge not to end the shutdown without wall funding.

Soy is thought by some, perhaps more on the right side of the US political spectrum, to cause "male breasts" and other feminine characters.

See articles such as Can Soy Feminize a Boy?

Is This the Most Dangerous Food For Men? There may be a hidden dark side to soy, one that has the power to undermine everything it means to be male

and

Soy is making kids "gay"

Alpha refers to being the alpha male or leader of a pack, and this role has been given to Ms Pelosi, who led the Democratic Party opposition to the continued shutdown. This represents another "role reversal" as far as gender is concerned.