It was suggested by a plumber, but is it common practice? The I joists are 11 7/8" but a 3.5 or 4" toilet drain line seems like a large hole to be cutting even if it's in the middle of the joist's depth.
Yes, this is common. The load in any joist is carried in the top and bottom surfaces (the flanges) of the joist. That's why I beams/I joists work. The thinner web between the flanges basically serves to keep the flanges at the same distance from each other. There is no load in the center of the web. Thus, the center of the beam does not need to be the same width as the flanges.
The manufacturer of your I joists has a guide for cutting holes in the joist, indicating how big the holes can be, where the holes can be located and how close to each other and to the ends of the joists the holes can be. I included an example below, but of course you should get the guide or template for your specific brand of joist.
Never notch the top or bottom flange of a prefabricated joist. If you do, you will compromise the joist.