Banning "fetus" and "transgender" is completely indefensible as they're fairly neutral words with no obvious replacement. But for the rest, imagine that rather than a ban this was a style guide recommending against certain words. The common theme in the rest of them is that they don't convey much useful information but have a strong emotional charge.
You don't need to say something is evidence-based, just show the evidence. Coming right out and saying your position is evidence-based just sounds like a way to shut down any objections, even reasoned discussion, by casting the other side as being against science, evidence, or facts in general. This is similar for science-based, vulnerable, and diversity. If you're seen as being "anti-diversity" your argument doesn't matter because you're a misogynistic racist xenophobe.
Entitlements is charged term because you've cemented your position on social welfare pretty clearly just by referring to them as entitlements. It's not quite as bad as Derry/Londonderry , but it's certainly not neutral.
I don't think any of these words should be banned, but I do think it would be reasonable for government agencies to use neutral language and fully explain their thoughts rather than using emotionally charged buzzwords.