Yet, Trump is rarely shortened to "Donald", Tillerson to "rex", Schiff to "Adam", Cosby to "Bill", etc..etc...etc..
Last I checked, "Trump" was shorter than "Donald", so I'm not sure why you would choose that example. However, I do often hear Trump referred to as "The Donald" by detractors.
In the other cases, like Cosby, the differences are small, the last names more iconic, and the first names very common by comparison (making it less clear who one is speaking of). "Greta", however, is a much less common name in English, and easier for English speakers to pronounce than "Thunberg". A good rule of thumb to apply in these cases is "Do not attribute to malice that which can be adequately explained by laziness."
First names only is often dismissive, and applied to women far more frequently IMO.
This is true, as far as it goes; but far from the whole picture, and applies mainly in the US. As counter-examples, I give you "Bernie" Sanders, and Hillary "Clinton", who are more often referred to by the quoted monikers than the unquoted.
Interestingly, the British in particular have a tendency to refer to public figures by diminutives of their given names, and doing so is considered affectionate rather than dismissive. When being dismissive, they're more likely to use the person's family name. EG. "Winnie" for Winston Churchill; and "Maggie" for Margaret Thatcher.