What disturbed the pagans about the Christians?
That in itself is a tricky historical question. But, broadly speaking, the first Christians stood accused of impiety. That word or its opposite is actually used often in the martyr-acts in the interrogation of the suspects, and despite the Christians protesting that in fact they were dutiful citizens in good standing with everybody, they could not go forward and sacrifice to the Emperor in order to maintain the peace. That is to say, their lack of worshipful regard for the spirits that were held to be the guarantors of social order and agricultural fruitfulness caused their neighbours no end of worry. Tertullian famously wrote (in Apologeticum 40): "If the Tiber rises so high it floods the walls, or the Nile so low it doesn't flood the fields, if the earth opens, or the heavens don't, if there is famine, if there is plague, instantly the howl goes up, "The Christians to the lion!" What, all of them? to a single lion?" Ha ha. Christians were labelled atheists because of their impiety.
I have mentioned Jeffrey Stout's definition of piety before:
Piety ... is not to be understood primarily as a felling, expressed in acts of devotion, but rather as a virtue, a morally excellent aspect of character. It consists in just or appropriate response to the sources of one's existence and progress through life. Family, political community, the natural world, and God are all said to be sources on which we depend, sources to be acknowledged appropriately.
We need to forget the use of piety in its strictly religious sense. In Stout's sense, there remains today a properly social piety: that 'just or appropriate response to the sources of one's existence and progress'. These may be entirely material: so, the nostrums of liberal order - free speech, rights, freedom of/from religion, equality and so on, need to be treated with due regard. They can even be sung about. It is interesting that 'good luck' or 'fate' still looms large in contemporary vision of piety, since whatever good fortune we enjoy is a result of the turn of the wheel in our favour. And so, modern culture is replete with sacrifices to fortune - in the form of gambling and divinisation; and also defences erected against the arbitrary turns of the wheel (life insurance anyone?). Also, the almost sacred regard family enjoys, even today, comes unexpectedly to those who continually rail against its demise. Environmentalism (rightly) appeals to piety in this sense.
Is it fair to say that Christians stand once again accused of impiety: for we give scant regard to 'luck', or ought not to. More importantly perhaps, we with other religious people threaten the fragile and hard won peace of our communities by bringing our beliefs to the table. Or, by becoming another special interest lobby group we cut ourselves off from our community and the duties of membership in it. We deny the absoluteness of family ties (or ought to); we shockingly tell young people that they ought not to pursue material goals or pleasure as their priority. By suggesting that all religions are not the same we again stand accused of threatening the social order, of inflaming 'religious hatred' or whatever...