Como dizer "dar mole (vacilar)" em inglês

The Western World is getting too lax with...

The Wertern World should be careful with the political biased speech... (or perhaps better "be careful with political biased rhetoric").

However, I am not sure about the reasoning of the writing as a whole.
Maybe it's about "the West being too accommodating with the rethorical 'self-serving' speeches of some Presidents/rulers?"

Plus, I don't think the United States was a Spanish colony, West Florida (at some time) was, but then was purchased from Spain (along with Louisiana purchased from France in 1803).
All in all the text had too much commas and was lacking full stops!

O mundo ocidental está dando muito mole para o discurso de viés político

The western world is shilly-shallying on the politically oriented speech.

Shilly-shally, as I learned, it's the "vai-não-vai", vacilar no sentido de hesitar em fazer algo. When somebody hesitates, wavering because it's unsure of what to do or is hesitant/irresolute.

Ref. merriam-webster

Could be, of course, but I think the question was somehow about "the Western yielding to the said speech/discourse. But it's me here, I am not 100% sure, written language can be tricky indeed...

Como expressão idiomática comum, eu usaria "sit on the fence".
Ref. dictionary.cambridge

It depends on the context, "shilly shally" could mean "take one's time", procrastinate, stall, hesitate, be uncertain, unsure, etc.