Remote self-destructible VM for browsing with Firefox in incognito mode (only sites you NEED to, that REQUIRE JS), through multiple VPNs over multiple proxies.
Everything else is command line HTML parsers (also on different, remote VMs), or API endpoints (HN API as an example?).
Need email service? Self-hosted, tiny email-server somewhere in eastern Europe. DDNS etc.
Local machine is always clean. Imagine you had to have iPad as your primary work machine? Very similar spiel.
Good thing is that most of it can get into a habit very quickly and most tedious parts can be automated :)
Keeping it up offline? Cash-only, prepaid phones (these give you internet access as well, 80$ no contracts, activate, use 20GiB until the end of the month, discard the phone, destroy and repeat), prepaid debit for "card required" purchases.
Easy-peasy! no idea what people are complaining about....