Based on what I've read so far in people's responses to my question it makes a kind of sense. If you convert to a different religion, historically speaking, you are now "out of competition" in terms of marriages, allocation of dowry, so on. So since many people historically never married across religion, there's no problem being nice to people who aren't competing for your same economic resources.
Please note that I don't mean to indicate approval for any of these things, just that historically that's how it has played out.
Hearing about a benefit of apostasy, from members of ones former religion no less, is quite surprising.
The perceived threat is from the claim that all other gods are false, which is one of the major factors in the anti Muslim/anti Christian sentiments playing out currently in India.
However, the attitude of muslims & Christians towards nonbelievers, idol worship and the historical violence and destruction wrought on them plays a bigger role.
A modern western atheist might carry the same "all gods are false", the vast majority of the Hindus will not have any problem with that.
I wouldn't take that statement at face value. They are definitely not freed from the social burdens of their station of birth.
They might achieve some sort of better treatment through their association with a larger group of Christians who together wield some political power and influence, but in matters of marriage and other aspects of domestic life, they will likely face the same discrimination that they did before conversion. Consider, for example, the caste system of Roman Catholic Indians in Goa:
I do find it fascinating how a converted Dalit is basically freed from the social burdens of their class. I would not have expected that, as most religious groups heap scorn or actual punishments on those who convert to another religion.