I would imagine that transporters needing the shields to be down is a matter of technicality.
Or of timing: shields might snap up and down much faster in the VOY era than in TOS.
However, the limitation against beaming through shields has always applied to beaming
up. The very first episode to introduce the limitation, TOS "A Taste of Armageddon", had people freely beaming
down in a situation where it would have been impossible for the shields to have been down even briefly (because the villains had sworn they would fire their death rays at the ship the very moment the shields dropped, and no such thing happened).
It makes sense for the limitation to be asymmetric. Phaser beams can lash out from the
Enterprise to the
Reliant, unhindered by the shields of the
Enterprise, but beams from the
Reliant cannot enter. It can't be a matter of "frequencies", either, as the
Reliant would supposedly have the very same sort of guns and could retune them after scanning for Kirk's own phaser frequency (a piece of information Kirk is handing over to them helpfully enough!).
Sure, sometimes skippers refuse to beam down people because of the shield issue. But "You can't go down there because we'd have to drop shields" makes sense even if only beaming
up is hindered, because going down would usually be suicide when there's no means of recovery.
As for beaming antimatter, the same limitation probably applies as with the "Unnatural Selection" biohazard: one has to make sure the containment materializes a bit before the contents. And dematerializes a bit after them, of course. Although what happens when both the container and the contents are in the form of phased matter, we don't know. Many episodes show phased matter still behaving as if it were intact (people are still alive and conscious, time passes, movement continues, machines keep on working). So basically the container would both have to remain behind a bit longer than the contents
and be in the phased matter buffer a bit before the contents! I'm not sure if that's really a problem in Star Trek terms, though: things can be in two places at once, or in two times at once, often enough.
There's also the case of the heroes beaming raw antimatter from vacuum to their container in TAS "One of Our Planets Is Missing". There was no container accompanying it
during the transport - it was sitting inside the ship and waiting for the antimatter to arrive. So annihilation apparently isn't a big problem in phased state...
Plus, on Voyager, shuttles (which contain mini warp-cores) were also transported aboard.
Just a nuance there: in DS9 "The Sound of Her Voice", it was a plot point that a vessel with a warp core could not reach the planet of the week, so a shuttle was used instead. And it was the
biggest shuttle found aboard the
Defiant, when the
smaller type was already verified to have warp engines and be capable of interstellar travel in at least two different episodes.
Does it follow that shuttles in general travel between stars without having a warp core aboard? We know runabouts have antimatter aboard ("Battle Lines" has the first dialogue proof and a plot twist hinging on this), but there's no comparable proof for shuttlecraft. Then again, "The Sound of Her Voice" might have referred to the fact that it's easier to rip out the warp core of a shuttle than the warp core of the
Defiant!
In any case, no episode dialogue has ever suggested that beaming antimatter would be impossible or even problematic. Indeed, Wesley in "Peak Performance" apparently did it without major special precautions, or else others would have caught on to the nature of the material he was transporting...
Timo Saloniemi