Asia is a huge area, so it’d be a bit hard to generalize about “Asian Catholicism”.
I can only speak for that corner of it which I come from, which is the southern part of India.
It’s difficult to divide Catholics into “conservative” and “liberal” here, because those labels aren’t commonly used.
On the good side, there are plenty of historic shrines (such as the two of St. Thomas in my hometown), a firm tradition of pilgrimages (such as to the Shrine of Our Lady of Good Health, about 3 hours’ journey from where I stay), and a wide variety of traditional devotions. There are regular Masses in the vernacular and in English, regular Rosaries, and a number of traditional Church activities (such as the Legion of Mary, the Society of St. Vincent de Paul, etc.) Most Catholics are regular church-goers, and there is formal preparation for all the Sacraments, conducted by the Church in collaboration with the laity. Many churches have an Adoration Chapel which is open round the clock. Some parishes are genuinely enthusiastic, and are able to reconcile tradition with technology.
On the not-so-good side, there is always a temptation towards liturgical abuses and syncretism - parts of the Mass are sometimes replaced wholesale by “solo vocal performances” from an enthusiastic priest, and improvised prayers are interpolated at times. There are also some who try to blend in gestures / rituals from Hinduism, but fortunately, this is a minority practice. Also, there is a lot of Protestant influence - most “Christian Music” that people listen to is Protestant, and a lot of Protestant songs are played during Mass.
On the down-side, there is a lot of indifferentism, and the “cafeteria spirit” has crept in too. Beliefs in universal salvation and that “all religions can lead you to Heaven” are common, and evangelization has fallen off (leaving the field free for any number of Protestant groups and even home-brew sects). There is widespread acceptance of the caste system (a regrettable legacy of our culture), with marriages and social cliques often formed on the basis of this. Marriage, in particular, takes a beating - the Church has tried to fight this by organizing compulsory pre-marriage counselling, but this is often very desultory. Contraception, sterilization, and even abortion are (tragically) not uncommon, and are often justified by their practitioners on economic grounds.
But if this summary sounds rather gloomy, I must hasten to emphasize that these are just generalizations. There is still plenty of room and opportunity for the Church in India to grow, and I believe that it will certainly grown stronger.
St. Thomas, pray for us!
Some additional information:
The first Saint of Indian origin, St. Alphonsa, was canonized in 2008 by the Holy Father, Pope Benedict XVI. The following page has a lot of details about her:
alphonsa.com/Content-1/SAINT-ALPHONSA.html
The church I regularly attend in Pondicherry, where I work:
sacredheartpondy.com/index.html
My parish church (I can’t find their homepage link right now; will post it later):
en.wikipedia.org/wiki/Saint_Patrick%27s_Cathedral,_Chennai