Okay...
So it all starts with universe building.
When you create a universe for your story you impose certain limits on what can or what cannot happen. You set the genre and the tone for everything else.
Mass Effect was set as a fairly hard sci fi universe where it was effectively set in a Universe much like our own but there was one additional element. Element zero, which allowed technology to exploit the Mass Effect. This was the important pivotal point of this universe and how it differs from our own. Important enough that it's the actual name of the series.
It was well though out, explained in depth and connected. All of the technology in the game follows through these rules laid down when the Universe was built. Mass Effect fields explain how the guns work, how ships can cheat the speed of light limit imposed on the galaxy. Why ship barriers only function against physical weapons, how some advanced materials are made.
The rest of the technology that's in the universe is realistic extrapolation from our current existing technology. Artificial intelligence, entanglement communication, quantum computing. All based in reality.
http://en.wikipedia.org/wiki/Artificial_intelligence
http://en.wikipedia.org/wiki/Quantum_computing
http://en.wikipedia.org/wiki/Quantum_entanglement
Look at the Thanix Cannon. This is a reverse engineered weapon from Reaper tech, basically a scaled down version of Sovereign's gun. It still obeys all the rules:
http://masseffect.wikia.com/wiki/Thanix
Even the Reapers as advanced as they are, are not so advanced that they can break the universe and others can copy/use their technology because they follow the same laws.
Throughout the entire series the only things that stand out as pushing the limits were Biotics, which were kinda weakly explained on how they worked but still obeyed the rules of mass effect fields. They dealt with manipulating force. And Indoctrination which is performed by various insidious means. They were still handled well enough that this doesn't push the audience's willing suspension of belief.
The Synthesis ending is on an entirely different level.
Apparently this device can let out a cloud of green energy which changes DNA. Not only that but apparently it's intelligent enough to change the DNA of trillions of different species without destroying them, but also to integrate biology into machines. Somehow it can alter DNA in such a way that it gives organics the benefits of machines and machines now get something that makes them alive and this solves a problem which is only introduced by a hologram kid which contradicts everything you've seen before...
If you've heard about radiation sickness you should know why changing DNA on any level is dangerous. DNA is basically programming for chemistry, there's no code for an arm or a leg. You can't just cut and past a gene for wings from a bird and graft them onto a human being because there are no codes for wings. DNA has a massive amount of information but cannot account for the location of every blood vessel or muscle strand in a creature. Screwing up the genetic code of a bunch of cells can cause them to replicate out of control, or genetic diseases can be passed onto the next generation which can lead to horrible malformations. Google image search radiation malformation. Not pretty.
A machine that changes the genetic makeup and chemistry of every being in the galaxy will have to physically transmute matter which is an ability nothing has shown before, then do it in a smart enough way that it can change everything in the galaxy then give them the supposed advantages that there's no more distinction between machine and man. The technology, processing power and knowledge to do this to a single individual, let alone a species, is staggering. Not only that but the problem it solves and the way it supposedly solves it is nonsensical.
How is it explained? It isn't. It simply does it.
Into Mass Effect's hard science fiction, well documented, explained and in depth universe you have just thrown a device which can do pretty much anything for no reason to solve a supposed problem in a way that makes no sense. It breaks the rules of the universe that have been laid down beforehand and it's a cheat created by poor writing.
It's a Genre busting device. It's as out of place in Mass Effect as some guy pulling out a cell phone in Lord of the Rings.
This is why we can accept Mass Effect based tech, they're science fiction because they obey the rules of the Universe. The Synthesis ending is magic because it breaks all of them.