"For whatever reason, the andhra men, women and many times, entire families convert from Hindu to christianity/islam"
Some personal observations on the Hyd/TS scene:
The Catholic Church has had a good presence for a long time in Secunderabad, probably came in along with the British Cantonment, and this is borne out by the plethora of St. Johns/Mary's/Patricks type schools which are highly regarded. Over time, they have built churches, schools & colleges in Hyd too and replicated the model. Their proselytism is somewhat passive, like subtly blaming Hinduism for caste evils, equating Hindu practices to paganism, criticising epics and puranas as being full of polyandry & polygamy, injustice, discrimination etc. They don't do it from a podium or a pulpit, but work steadily, subtly on individuals/families at a time. Education is a big business for the Diocese, and allows them to show a benign, respectable face to lakhs of students every year. The depiction of Xtian priests in Telugu movies has always been benign and Gandhian. There is of course inducement of jobs and financial help as well to attract converts. Those who convert often retain hindu culture and customs, to the extent of keeping bindi, sarees, mangalsutram, flowers in hair, even aarti and agabatti to their home Jesus on Cross statue. Their names are semi christianised like Paulraj, Thomasamma etc. or Indian names that don't tie back to a Hindu divinity like Dayanand, Premkumar etc.
Then there are Non-Catholic Pastors who preach different flavours of Xtianity, Protestant, Adventist or otherwise who have appeared in the 90s I'd think, and they are more aggressive, their inducements also include immigration help to US, Canada, UK, AUS, NZ which many find attractive. These converts typically adopt full Xtian western attire, names and customs, and within 2 generations all traces of Indianness are gone.
They all take some pride in converting educated FWD castes like Brahmins, Reddys, Kammas which fill their ilk with people with means and reach.
Most of the conversions, FwdC or BC or OBC happen when a person or family is going through tough times like serious illness, tragic incidents, deep financial trouble etc when they are feeling lost, vulnerable and receptive to words of solace offered by someone nearby come from the Bible - "Read a few Bible verses like you'd read Hanuman chaallisa, whats the harm? " ! Those who convert have been convinced that the new Christian devata will solve their problems (which a Balaji or Pochamma thalli won't) and/or that they are switching to a more modern, non-discriminatory and superior, therefore dominant "world" religion. However this doesn't apply to dowry or caste discrimination
they mostly continue as before, divorces are easier.
There are some inter-faith marriages now and then, in these cases, there is some pressure on the hindu boy or girl to convert but its not as intense as it is with muslims. But the children mostly end up non-hindu.
There is a degree of focus on conversion in rural Telangana, but as pointed above, those OBC poor folks practice a kind of folk hinduism anyway, where superstition and village customs matter more than ideological or theosophical underpinnings, and they may not care to convert. The focus of conversions in AP OTOH is very active aggressive, especially visible in towns and villages as I noticed during my travels. Can't say if they follow the same methods or have innovated a lot more in AP.