Hmmm.... I'm muslim sunni, and somewhat apply NU's way in traditional religious rituals, but tend to be more in tune with sufism, rather than mainstream Islam, or any puritant view of Islam (especially the strict Wahabbism

).
And I really don't like people who forced their interpretation of religion to others. Monopolize the "truth" as theirs own, etc. Try coercively to "save" the soul of others from eternal damnation (puhleeze, keep your faith for yourself).
Wisdom is from God, and God is benevolent, nobody can claim that the love of God is solely theirs and their sect only, while others are condemned to hell.
Oh yeah about NU-Muhammadiyah things. In Indonesia majority follow Sunni mainstream, Shiite do present in Indonesia although really small and insignificant. The division of Sunni-Shiite IMO is purely politic generated dispute, about Ali the successor of the prophet Muhammad. Other Shiite tradition developed later; faith, beliefs, rituals are merely to impose their claim as "true" successor of prophet and Islam.
In Indonesia Shiite sect is present, although not significant in numbers of follower. But the division of Islam school in Indonesia is clearly shown between Nahdlatul Ulama (NU) and Muhammadiyah. Both follow Sunni majority.
NU is majority in Indonesia. NU is Traditionalist, which means they used traditional method and reverance to their Ulama or Kiyai in the matter of religions. The unique thing is the term traditionalist doesn't means traditional puritan Islam in the middleeast. NU already infused and incorporated traditional rituals that not belongs to Islam in Arab. Which is already incorporated native tradition and rituals into Islam. So clearly NU shown native Javanese influence and incorporate it in to Islam. The example is "Selametan", is traditional religious occasions involving feast of food and reading of Quran (pengajian), this "selametan" can be incorporated in to Nujuh Bulanan (Pre-Maternal ceremony, originally a Hindu tradition), Sunatan (circumcisions), Blessing the new house, Newborns, Tahlilan, 40-harian (a reciting Quran ceremony to blessed the deceased person), or any thanks giving to God occassions (syukuran). This traditions probably already exist in pre-Islamic Indonesia (Hindu-Buddhist or even Animism traditions).
On the other hand Muhammadiyah is the movement to establishd "pure" Islam. Islam that free from "corrupted" non-Islamic influence and tradition. Soo Muhammadiyah never held "selametan" since they view this as merely waste of money or energy, or simply not the way prophet did. Muhammadiyah discard traditional value and traditions, and solely rely on Quran and Hadith and try to move into puritan Islam. "Muhammadiyah also tends to applied more scientific approach (as long it's not against Quran). However this "modernist" movement in the same time held more "sterile" Islam.
The disputes between those two especially aroud petty issues of rituals, disputes may about simple short formula of prayer during Shalat Shubhuh, NU followers that felt offended, if Muhammadiyah followers refused to take part in communal selametan, and even went far by saying that selametan or any traditional things are un-Islamic, too much or "bid'ah". Or the dispute may arose around the determinations of the first day of Ramadhan. NU tends to use traditional astronomic way to determined the new moon by observing "Hilal" or the new crescent moon. While Muhammadiyah tends to use "modern" mathematical way to calculate the Islamic calendars.
That's just what I know so far.....