I got my guitar set up and the luthier did an amazing job. However, I want to know if the magnetic part of one of the pickups sticking out is normal. Beneath the A and D strings, these parts stick out to the point where sometimes I feel like I really have to pay attention to not hit that area, since there is resistance when the pick hits and it messes up everything. Maybe I just need to get used to it, or is this relatively common? Thanks.
Some pickups are designed like that, so it's almost certainly normal.
But if you hit it with the pick while playing, you should probably lower it a bit. Lower it equally on both sides with the two screws at both ends, a bit at a time, until you can play without hindrance.
The volume from that pickup will decrease, but only a bit, so it shouldn't be a problem. And should you want to put it back where it was, you can always do it.
For reference and for convenience, take a few photos that show exactly how your luthier positioned everything, so you can easily go back to it later on if needed.
And one more thing: if the pickup magnet is too close to the string, its magnetic field may alter the string's vibration! The string will not vibrate freely and sound as it's being choked. Sustain will drop dramatically. And by looking at the photo, those magnets look too close for comfort to me. I'd definitely try lowering that pickup to see if the string then vibrates more freely: if the string seems to have more sustain when you lower the pickup, it definitely means that it was too close.
In case you think of pushing down those taller magnets to level them with the rest - even though it's probably possible, and only a matter of pushing them down, don't! Why not? First of all, they have been designed that way for a purpose, and changing it will only make things worse. Secondly, you could break the pickup -- like I did on an original '66 strat when I was a kid and didn't know any better. The pickup's copper wire is wound tightly around those magnets, and if you push them around there's a good chance that the internal friction will break some of that wiring -- which is exactly what happened to me. My guitar (like all 60's strats) had all the magnets at different heights, higher in the middle and lower on the sides, and I cheerfully pushed them around a few times, to find out how the sound would change. Well, I don't remember how the sound changed, but I do remember that one pickup soon stopped working. By testing the wiring, the ends were no longer connecting. It was clear that somewhere inside the wire had broken. Live and learn... (and pass it on if possible)
This is very common and has a direct impact on the sound of the guitar.
As the core of the magnets will get close to some of the strings, these strings will sound louder. However since the core is magnetic, they will take some energy from those strings and you will lose sustain.
The thicker strings have more mass and will naturally have more sustain, so it is not uncommon to bring the cores closer to them so you get better bass response without affecting the sustain much. The effect would be more prononced on the treble strings.
The wiring around the metal core is very (very) thin and you can break it if you try to push it. I have seen some pickups where you can rotate them as you push / pull them, but I'd get a spare before trying to do it. This is not meant for manual adjustment.
It's better to adjust the whole pickup: you can lower or lift both sides independently. Unless you have tone issues, the only time it makes sense is when you are changing the string action. You want to strike the right balance between loudness and sustain, but realistically, the sustain issue is not dramatic while the sound difference is noticeable with the distance.
In the past, I have filed some of them down. It will change the frequency response, but either I'm old or it's not noticeable in audio (on a frequency analyzer you would definitely see it)