All 11 of M81's companions are redshifted with respect to the larger, gravitationally-dominant host. Want to venture an explanation of how that can be the case?
Sure thing.
M81's companions = Hubble flow + peculiar motion
M81 = Hubble flow + peculiar motion + weird blue shift
As far as what causes the weird blue shift, it's not hard to imagine.
Suppose M81 has an exploding shell of gas or massive jets spewing out.
You'll see the blue shifted part coming toward earth, but not the red
shifted part going way, since that is hidden by the rest of the
galaxy. Take a picture of M81 and imagine two jets coming from the
core. You'll see the one coming toward you, but not the one on the
other side of the galaxy.
I'm not an exgal-guy, my background is in supernova with a smattering
of accretion disk knowledge, but this sort of thing happens all the
time.
Is it possible that all 11 of M81's companions are rushing away
from the Earth?
If I'm right about this then you are using the wrong baseline
here. M81 companions are the baseline, and M81 is weird.
BTW, if you think that the main galaxy can be "massively blue-shifted" then you ought to be prepared to explain why that might be the case.
We are looking at what sort of velocities? 1000 km/h? Accretion disk
jets can pump things to close to the speed of light. Getting 1000
km/h because you can see the stuff coming toward you but not the stuff
going away is not a problem.
Grasping at blue-shifts for host galaxies while denying the reality of red-shifts for companion galaxies is a bit ridiculous.
See above. It might wrong, but I'm not grasping at straws because you
see this in accretion disks all the time. If you have a central
object then the gas around the central object will appear redshifted
with respect to the central object, but you have enough resolution to
figure out what is going on.