Not so many years ago, many if not most animal advocates would talk about other animals in term of "it." Some still do - it's a habit that is stubborn and hard to break free from, and supported, of course by the oppressive ideology of speciesism. It seems fairly common that animal advocates still refer to a nonhuman animal as "that."
Nevertheless, speciesist language is something we as a movement are improving on. Ableist language remains a major problem - one that I believe needs attending to.
Here's one brief account of how people may be effected when others use ableist language.
I have a great-aunt who had this label ["moron"] and was warehoused in state hospitals for much of her brief 25 years of life. So when I see this word, it resonates through history. I remember all of the people with this designation who lived and died in state schools and state mental hospitals under conditions of extreme abuse, extreme degradation, extreme poverty, extreme neglect and extreme suffering from disease and malnutrition. My great-aunt lay dying of tuberculosis for 10 months under those conditions in a state mental hospital. The term moron was used to oppress human beings like her, many of whom are still in the living memory of those of us who have come after.
Moron -- and related terms, like imbecile and idiot -- may no longer be used clinically, but their clinical use is not the issue. They were terms of oppression, and every time someone uses one without respect for the history of disabled people, they disrespect the memory of the people who had to carry those terms to their graves.
Note how the writer is saying that oppressive terms may remain oppressive even if they no longer have the same meaning. This may apply to words with multiple meanings. This is why we should not argue when people say that they find a word or phrase triggering and upsetting. The fact that they are saying it should indicate that this is an issue for them . I'd say that everyone would hesitate about using the phrase "you spaz" just because a modern use for it became popular.
It seems that ableist language is as common and embedded into cultural norms as speciesist language is - perhaps even more so.
So, let's try to be good allies, and let's at least begin to question, call out, and try to eliminate ableist language from the animal advocacy movement.
A lot has been written about why the "animal movement" are not good at forging alliances with other social justice movements. Indeed, it is not clear that the animal advocacy movement is recognised as a social justice movement, even within large parts of the movement itself.
There is sexism, racism, often fascism, and certainly ableism in the prevailing animal advocacy movement - and we wonder why justice activists shun us, or think we are politically shallow, or accuse us of being a single-issue?
If we want to make progress; if we want to have a dialogue with (other) progressive movements, we need to radically sharpen our tools.
THIS is a useful site to visit when looking to avoid ableist language.
 It seems to be the case that some believe that this apparent concession to the "politically correct" may be used as a means to silence critique. This does seem to be a possibility. Perhaps we need to assess such a possibility on a case-by-case basis but one thing we cannot do is use this possibility to reject the idea that we should ignore the harm ableist language causes to individuals and/or groups.