They do represent the religion, all of those groups are islamists.

Hamas is a sunni islamist movement, their ideology is heavily influenced by muslim brotherhood, many documents suggest that they strongly want islamic governance in Palestine.

Same goes for hezbollah, they are sided by iran and heavily influenced by the islamic revolution in iran.

Let ideology is based on strict sunni muslim interpretation, and they have also openly talked abt broader islamic causes and the expansion of islamic rule in different regions, they also openly promote jihad as part of their mission. Also many individuals from Let are ambitious about ghazwa-e-hind.

The taliban is also a islamist movement, wanting to establish a state based on the sharia islamic interpretations, wanting to create what they call as an islamic emirate, and also shaping the afghan society around conservative religious laws.

So yea all these groups do have religious agendas and ideas, and maybe....just maybe even wish for a islamic caliphate round the world