Learn English – the correct use for “practised”

The verb consist is never used without a preposition and it usually takes either of or in. In your example, it should be consist of. Thus, the first sentence is correct while the second is wrong. From the Oxford Dictionaries:

1 (consist of) be composed or made up of

• (consist in) have as an essential feature

2 (consist with) archaic be consistent with

I should also add that it is probably not uncommon for some speakers to drop the of in conversation, but this should by all means be avoided in written contexts.

The either version would imply two (2) choices, whereas any would imply multiple choices. While two is a multiple — so any could be used — I prefer either when referring to a specific two choices.

The use of any additionally implies no use outside of the offered subset. So if there is a superset of choices beyond the subset then "They don't use any of them" could imply no use of the superset either.

For example:

— Do they prefer Ford or Chevy cars?
— They don't use either of them.

This defines that they do not drive Ford or Chevy cars.

— They don't use any of them.

This may be taken to imply that not only do they not drive Ford or Chevy, they do not drive any cars at all.

— They don't use any of those.

This removes any perceived implication of the superset.