Shifting the tuning around to suit the situation is common practise, but you need to be familiar with the flaws in Equal temperament and how Just Intonation works.
Take a bluegrass band as an example, the fiddler will often tune the open G straight and stack perfect fifths on that G (701.9 cent intervals instead of Equally tempered 700 cents), making the open E string sharp of ET by 5.7 cents.
Out of tune? Not really, as fiddlers say "better sharp than out of tune"
(Sweetener FDL).
A concert violinist will tune differently with the A string tuned "straight" and the others tuned in perfect fifths above and below the A (Sweetener VLN).
The Dobro player will invariably lower the B strings by the full 13.7 cents to get a pure beatless third (Sweetener DB0).
Does he worry about "blending in"? No, it's about sounding good - he just watches
when he plays
what, those sweet triads are worth it.
The banjo player will also lower the B string a smidge (about halfway between an Equally tempered third and a Just intoned third - Sweetener BJO).
Then there's pedal steel, with three different pitches for F# etc. (Sweeteners SE9, SC6 etc.)
It's all about having your instrument sound as good as possible within itself while being aware of the general tonal center of what's being played.
Equal temperament is a distant object in the rearview mirror at that stage...it's a good basis, sure, but trust your ears.
What sounds good to you is probably going to sound good to others too, just be aware of how tuning works.
Our tuners are just the programmable assistants which can show you visually how to get to what your ears
want to hear, when your ears
can't hear (e.g. on stage).
Purely IMHO of course
.