I sometimes see the book Reliance of the Traveller, or Umdat as-Salik, mentioned online (Wikipedia; Amazon). Judging from Google, it has found a role as a go-to manual for those who wish to criticise Islam, with the top hits including "Creeping Sharia", "ConCit", "Islam Exposed", "counterjihadreport", "Mapping Shari'a", etc. This may be predominately because of the book's online availability in English, and I would guess that native English speakers tend to have a more Islam-negative attitude than the general population.
Question: Does the book "Reliance of the Traveller" play a significant role in Islam?
I found an online Shafi'i fatwa which gives the book a glowing review:
It is really hard to praise this book enough. It stands, without equal or competitor, as the primary Sunni manual of Islam in English. -- Moustafa Mounir Elqabbany, Qibla.com, sourced from IslamQA.org
And one fatwa with a luke warm stance (outside of the Shafi'i fiqh):
There is no harm in Shaf'iee laymen studying the book provided they refer to a qualified and reputable Sha'fiee Mufti in personal fiqhi matters. As for Hanafi laymen, it is not advisable to study the book since it can cause confusion and lead one towards Talfeeq, i.e. picking and chosing between the different Maz'ahib. This is Haraam as it involves probing in matters of Shari'ah without possessing the authority to do so. -- (Mufti) Abdullah Patel, MuftiSays.com
...This translation has led to this work becoming influential among Western Muslims. -- Nuh Ha Mim Keller
So maybe it's important in the Shafi'i madhhab, and growing in influence among Western Muslims since it's in English and easily downloadable.
Now having read a small part of the book (it's very long), I'm finding it is quite a handy reference.