I'm not sure what I'm looking at (lol). Moog has changed their BJ boot design at least twice. I don't understand what you mean about one side having a washer, unless that's a washer I'm looking at and thinking it's just grease? See arrow on pic below. On same pic, to me it looks like the lip on the portion with the greatest outer diameter, is not cast well and just rough, or is that where the washer is?
What Rock Auto currently has pictured, has a metal snap ring/something at the top of the boot (stud end) that grease would come out of if too much was put in, but there could instead be a tear in the boot... Moog boots are notorious for this, but other brands susceptible as well.
I know on some, the boot had a molded in notch, or arrow or something, so when you get the BJ alone this helps to orient the grease valve 180' away from the brake rotor to minimize throwing grease that direction, but their separate BJs don't, and haven't for a while, had a boot similar to what you've pictured.
For example Rock Auto's listing for Moog PS front lower control arm:
Different boot than on their PS lower BJ alone, and even this is different than the more recessed boot redesign that I got (same part K8695T) a few years back for my '98:
Is the same amount of BJ stud threading, sticking through the other side of the steering knuckle, or is it possible one of them (the right one?) didn't fully seat in the knuckle due to corrosion or low nut torque? Is it possible one was not greased after installed or had more put in it?
From the picture, right now they both look fine from what I can see, except for the excess grease. I'd wipe that off and wait a while to see if it goes flat again, though if it hadn't been driven when the pic was taken, movement of the BJ may squish a bit more grease out. However if it is coming out the bottom of the boot (green arrow in picture), and only there, it doesn't seem to be a problem, is where it's supposed to come out.