Infinitive use in “whether or not he be” compared with its use in “if he be”

Here is the phrase in question:

. . . but whether he be, or whether he be not. . . .

Is the usage of the infinitive in that phrase above the same sort of thing as occurs in this quotation:

“Whosoever holds this hammer, if he be worthy, shall possess the power of Thor.”

Are those two uses of the infinitive be the same syntactically, or are they different constructions altogether?

I find it rather weird that this formal or archaic usage coincides with the colloquial use of be as in

“Dudes be like. . . .”

Is this last quote perceived as a new colloquialism, but in fact has roots stretching back to Middle English (like for example the word ain’t)?

I’d really appreciate it if you could both parts of my question.

The uses of be in your first two examples you cite are not an examples of an infinitive but rather an example of the English subjunctive mood. The third example example is a colloquialism that uses the subjunctive form of the verb to suggest that the dudes being referenced are not actual persons, but persons being imagined by the speaker.