Many talk show hosts have pretty wide ranging scope for their on-air remarks. Here in greater Lost Angeles, we have one station with big listener stats, with Limbo until recently. 640 am KFI
Another with Levin, etc.
But often, a personality goes beyond the tastes of the station owner, and the owner usually has a clause to terminate the personality "at will."
Joking about transgender people apparently triggered that boundary, here.
A topic which might likewise trigger a boundary: joking about Mothers Against Drunk Drivers," which I have read some pretty bizzare things on "conservative" forums.
The station owners is within his rights, to stop employing people who violate good taste.
These jokesters ought to look up "intersex" and get a physiology and biology lesson. That would be a sub-category under transgender, for example--an individual born different, at no fault of themselves.