Where do you even start. Firstly, this is just a law Amber Rudd wants to make, it's not anywhere close to being made into actual law, it's very unlikely it will be. It's probably more a bit of signalling/posturing by Amber Rudd to appear as the "Tough on extremists" candidate in the forthcoming Tory leadership (and hence Prime Ministerial) election.

Secondly, even if this law was passed, it would never be actively used against the public. It would be used to throw more charges at people they have arrested already, or to have some charges to throw at people who they have arrested but can't charge. It's a handy catch-all (along with vague bans on pornography) that criminalises many normal people who have internet-connected devices. It means they can haul you over at Heathrow, search your device and say "Ah! You've looked at this naughty thing! Too bad!", for example - giving the state an easy way to reject people they don't like much more easily.

A lot of this approach stems from Theresa May herself, who spent many years as Home Secretary struggling to deport Anjem Choudary.