Q:

Any other example of "socially stigmatized phoneme" like the "th" sound in some Venetian dialect?

Older people living in some rural areas north of Venice use the voiceless dental fricative /θ/ for many words, like cena "supper" which is pronounced θena, exactly like in Spanish cena (Castilian, not Latin American) while in Italian the pronunciation is t͡ʃena. Other examples can be graθie for grazie, θereza for ciliegia "cherry" and so on. 
The /θ/ sound was allegedly introduced by a Greek saint during his evangelization of those areas, and it remains as a legacy of his origin since it corresponds to the Greek letter theta. I've read than one can even trace the path followed by the saint by looking at the places where this sound is still being used, from Venice and up to Padua, Vicenza, Treviso, and Belluno in the Alps mountains. Towns located a few miles apart didn't adopt the theta at all. 
I don't know whether this story is true or not, but I'd be happy if it could be confirmed! Anyway, despite its respectable origin, the /θ/ spoken in those parts of Italy is today unequivocally associated with poorly educated people, especially of older generations and living outside the big cities. The Venetian dialect and its variants are still widely used throughout the Venice region, including every urban area, but the vast majority of people never use the /θ/ sound, which has a decidedly "peasant" connotation. It is generally replaced with /s/ or /tz/, so in the example above θena becomes sena, which is perfectly acceptable in any conversation and in theatrical works spoken in dialect, where the use of /θ/ is absolutely out of question!  
This stigmatization may be difficult to grasp for English or other non-Italian speakers, but it makes perfect sense for an Italian as it doesn't exist in our alphabet and it is so distinctly different from all the other phonemes we use.
My grandparents didn't speak with the /θ/, but sometimes they'd throw in words with this sound to stress the fact that they grew up pronouncing words this way but then they became more educated, and also to mock people that still speak in dialect this way! 
Is there any other example of phoneme stigmatization, not necessarily associated with the level of education but in any other context?

A:

In any place where regional origin is associated with lower social status (basically, where internal migration in search of jobs and wages is/was important, or where a central political authority was recently imposed into a periphery) we will find such phenomenon.
Some from Brazilian Portuguese:
"ti" pronounced /θi/ instead of /t͡ʃi/ (very much the same as in your example, btw, except that both pronouciations only exist before /i/) shows a Northeastern (more specifically, Recife-an) pronounciation; as there was intense migration from the drough-afflicted Northeast to more economically dynamical Rio de Janeiro and São Paulo, which lead to a significant part of the working class in these cities being of Northeastern origin, and so to speak like this, it resulted in the pronounciation being stigmatised.
Non-stressed "e" pronounced as /ɛ/ instead of /e/, involving the same regions and "logic" as the previous;
Post-vocalic "r" pronounced as a retroflex is characteristic of the hinterland of São Paulo. As there is always migration from the countryside to the capital, and the rural areas have a low prestige, again this pronounciation is stigmatised.
Final "e" pronounced as /e/ instead of reduced to /i/ is similarly characteristic of rural Rio Grande do Sul, and as such stigmatised in a similar way (though in this case, due to the importance of the rural area in the identitary mythology of gaúchos, it gets more complicated, the pronounciation being derided by inhabitants of Porto Alegre when uttered by migrants from the countryside, but upheld as a source of pride against people of the centre of the country).

A:

In Hindi the usage of only /s/ in the place of /ʃ/ /ʂ/ and /s/ generally makes one sound less educated. Same with the realization of the monophthongs /ɛː/ and /ɔː/ as diphthongs /əɪ/ and /əʊ/. These are mostly found in rural areas that don't use standard Delhi Hindi (also called Khadi Boli), speaking e.g Haryanvi, Bhojpuri, Braj Bhasha etc.

