As far as I know, in D&D, you don't summon familiars and unsummon them all the time. You summon them once and then they stick around. Maybe you can put them into your backpack, but they're still around.

So why does every PC tell me to "unsummon" my eyeball/mini-dragon/pet lemure? What's the DM ruling on this?

Is it acceptable to RP the "unsummon" command as it should be in P&P, namely as simply putting the familiar on your shoulder/into a bag/whatever? I'd be rather fond of NOT putting, say, a rat away but instead having it on the PC's shoulder at all times, like you'd expect it with a real familiar in P&P.

Is that acceptable?

Bump? Just today I saw some druid asked to "unsummon his companion"... But you can't unsummon them in D&D. They're always there. They don't phase in and out magically.

How do I deal with this IG? Or should I just assume that in the EFU canon, ACs and familiars ARE indeed summoned and unsummoned at leisure?

If someone tells you to unsummon your familiar/companion, just emote sending them away or putting them in a cage or whatever you want.