Is it acceptable to mix Latin with English?
Solution 1:
Since persona non grata is a well-known Latin term by English speakers, at least those more educated, it is proper to use it in an English sentence, as long as you have a reason. As I already mentioned, not every listener may understand the phrase. Use it if you want to sound educated, but keep in mind that there is an English alternative which you can use to make it possible for all listeners to understand the phrase.
This applies to all Latin phrases used in English. Choose your words wisely based on who you are talking to. That's the golden rule!
Solution 2:
There are a few different ways in which loan words or phrases are used in English, whether from Latin or otherwise.
On the one extreme, there are words like potato, cello and waltz that are so absorbed into the language that their being loan-words is more a matter of the history of their etymology, than it is of how they are used. They may leave a trace of their origins in unusual sounds or spellings or in rarer cases retain a diacritic even when used as fully English words, (façade, naïve, cliché, and more rarely, rôle), but often only those with an interest in such things would even know they were loan words. Use freely.
Close to these are words that are more obviously loan-words, used because no fully English word conveys the same meaning as clearly, and they are very well understood. Use freely in English, but beware that many are "false friends" when it comes to learning another language (mousse is only some sort of creams in English, any in French, and several words from Japanese used only in relation to sex acts in English are — to the point where I won't give examples — quite plain and boring words in Japanese that only refer to sex acts when that is clearly the context).
On the other extreme, you could just throw in a Latin (or French, or Cherokee, or whatever) phrase and it would be a valid switch in languages, but only useful to someone with the same facility with that other language. Use where clearly appropriate only.
In between, we've a few different cases.
There are some like et cetera that are close to the loan-word case above, in being used and understood by just about every fluent speaker, but which are still seen as foreign. Some commonly used abbreviations would be examples here, with i.e. being understood by people as "that is" even if they wouldn't recognise the unabbreviated id est. Likewise, etc. would be even more immediately parsed than the full et cetera. In the case of e.g. some even re-interpret it as the fully English example given rather than the exempli gratia it actually stands for.
There are cases where a phrase is used with an understanding not just of its literal meaning, but of the history that goes with the phrase. Hence if someone says Carthago delenda est they are presumably not calling for the destruction of Carthage, but implying that they feel as strongly that the topic of conversation must be fully ended as Cato did of Carthage. More directly, carpe diem has no advantage over sieze the day in terms of its metaphor; indeed, to English speakers the more literal translation "pluck [as in fruit or flowers] the day" is inferior to the sieze that is more often used. Here, we use carpe diem because it is so widely used that it has gone beyond cliché into idiom. We are confident that the audience are familiar with the arguments in favour of the sentiment (because of how often it is used), and we want to bring them to mind.
There are cases where a phrase has a very specific meaning, and we wish to use that specific meaning precisely. Legal terms, eclestiastical terms (most often of Roman Catholic origin, though the 5 Solae and each of their individual names such as Sola fide would be Protestant examples) and terms from diplomacy and war.
Here we are looking for the positive benefit that jargon can bring — precision within a field. We may or may not incur the negative effect of jargon — confusion to those unfamiliar with the field, or who even use the same term differently in a different context — depending on how well known the phrase is and whether it has another meaning. Often that precise meaning exists more strongly as a borrowing: In Latin, casus belli could mean anything that caused a war, but when used in English it would refer solely to the legal justification given for a war and hence the argument that it should not be seen as a war of aggression by the international community.
That possibility of another meaning could be from it having a different, similarly precise use in another field, but it can also be from yet another case. Words and phrases undergo mutations in meaning, as many posts on this site will attest. Sometimes this can happen to a loan-word or loan-phrase. As noted elsewhere, persona non grata is an example of this, as it has a precise meaning but is also used colloquially within English.
Similarly, we have phrases that aren't even correct in the source language. Some Latin borrowings are "schoolboy Latin" and not actually correct (though usage of such phrases is increasingly rare these days, presumably because so are schoolboys learning Latin). An interesting case is that in English we use nom de plume where the French would have used nom de guerre. As such, nom de plume was really an English phrase composed entirely of French words! So common is it, that it has now been borrowed back into French.
In each of these cases it is probably best to balance likely familiarity (including favouring i.e. over id est), necessity of precision, aesthetic judgement and how well plain English could serve, in deciding whether to use the phrase.