Recently I participated in a project where we played film music live with the film playing. We got an earbud that played the click track for one ear so we stayed in time.
Now this was an amateur project and my first time playing to a click track. It seemed to me that the click was more distracting than helpful. I started out by kind of trying to ignore it as much as I can because I had trouble hearing the orchestra clearly. As we practised more I got somewhat used to it and saw the advantages it brings, especially if you play along a film where you absolutely need to stay in time for the whole thing.
There was one issue I had until the very end though. I wasn't able to adjust the intonation as well as I usually would. I knew when the intonation was off but I was simply not able to know the cause. I usually can tell if I'm too high or low but with the earbud in I felt lost.
I put the earbud in my right ear and I was sitting slightly to the right of the orchestra so my left ear was directed more or less at the middle of the orchestra.
With some practise it got better but it was nowhere near playing without the click.
How do the pros handle this? Is it just a lot more practise with clicktracks or do they take out the earbuds for parts where intonation is very important? I imagine that intonation is much less of a problem at a certain level of play but I assume they still need to adapt their playing during a piece.