The rules seem to give little indication if the blindsight gained by the Fighter's Blind Fighting is actually able to automatically foil high-level illusions (such as Major Image). But this text from the spell seems the most relevant:
The image appears at a spot that you can see within range and lasts for the duration. It seems completely real, including sounds, smells, and temperature appropriate to the thing depicted
To me, this sounds like that Major Image automatically foils blindsight, unless the character makes a successful Investigation check (but this burns the character action). If my interpretation is correct, this would imply that Major Image (assuming no caster is actively controlling it), while most of the time it is seen as something "static" and "non-reactive", actually does have a reactive part in it regarding perception (even special senses).
My example is the bat echolocation. Suppose there is a permanent Major Image of a 20-foot cube of stone, and we will also assume that no caster will be actively controlling it. The moment the echolocation range comes into a square affected by Major Image, the spell would reactively reflect sound waves, just as if it was a real stone cube.
My doubt comes from this next part of the spell description:
Physical interaction with the image reveals it to be an illusion, because things can pass through it
The problem, here, is that basically anything regarding perception is a physical interaction. After all, humans see things because light is reflected of objects (or some objects themselves, such as stars, emit light). But perception is indeed physical interaction - I don't see any way around this. Of course, this would make Major Image useless even without blindsight, since normal sight is physical interaction with the object you are seeing, and I don't think this is the intent of the rules.
Thus, my interpretation here would be that the text above refers to physical contact rather than interaction, implying that creatues or solid objects can pass through the illusion, releaving the "stone cube" to be a fake. But there are possibly exceptions to this, such as the illusion of a fog.
And now comes the "things can pass through it" problem. If we interpret "things" as meaning "solid objects" (like arrows) or even spells, that's a thing, but what about light and sound? Does the Major Image let the sound waves of the bat echolocation pass through it - but this would automatically reveal the illusion - or does it react to them, reflecting them?
My interpretation would be that Major Image does need to react to light, sound and temperature, otherwise normal sight/hearing would foil it automatically.
I have read (in the thread linked below) that this is DM call, but I am the DM in a campaign, thus I would like some feedback on how this is ruled by others.