Do I have to level up the trust level with all squad members to get the good or best or whatever ending?
Or can I stick with my two favourite crew members for the whole game? (except the parts where I'm forced to switch like going back for the rescue etc.)
I've reached upper Tokyo and used Bo and Rachael so far. They're trust level 4 and 3 respectively. I'm planning to make a second playthrough with a different squad setup.
Should I start using other crew members now or can I stick with Bo and Rachael to get the good ending?
Two members alone won't do it, you need three bars of trust or more for the whole Rust Crew. There's not so much need to worry about Shindo's trust level too as there's a bit in chapter 5 where you have to play with him and it's very easy to farm his trust by staying where you are and repeatedly killing the waves of enemies that come while he and another character are both working on opening a door, that happens twiice.
If you intend to do another playthrough though I'd suggest just playing with whoever you like, on your second playthrough it'll be easy to get everyone's trust levels very high or maxed if you farm with certain people at certain points.