If ISPs can do this, then how would my anonymity be affected?
TLDR; your ISP could find out, still they can't see what you're doing.
Your internet service provider (ISP) manages your connection to the Internet, thus receives everything you send through that connection.
Your ISP will be able to figure out that you are using Tor, as you therefor will have to connect to a Tor entry node. After the Tor connection is started by TAILS, your traffic will be anonymous though.
The TTL (time-to-live) contained in IP frames emitted by a system usually leaves clues to the general type of OS used (Linux / Windows / MacOS), but this should not allow for a specific association with you using TAILS.
If your ISP actively monitors your traffic to find out you are running TAILS, he likely could: Not from the traffic your system forwards, but from the fact that your TTL matches that of a linux and your traffic is very light, except for the one connection to Tor.
As a countermeasure, you could run a regular windows machine, with TAILS virtualised in a VM. That way your traffic looks less suspicious, however, it includes other risks.
No, the only thing your ISP can figure out and try to block is that you're using Tor network. But - never the less - it's not how it's intended to be by design: like 10-20 years before we all have had an ISP LAN direct connectivity, but now it's mostly gone for the sake of censorship. So - the only reliable way to be truly protected "in a Tor way" is to start building home LAN's by hand again: nobody can interfere into the switch placed in the multi-flat house or a Wi-Fi between houses, if it's a p2p operated network.