I'm going to my source for this, one I've cited here before, the Star Trek: The Next Generation Writers' Technical Manual, Fourth Season Edition. This was sent to me directly, in a pitch package by the ST:TNG Script Supervisor Lolita Fatjo. This is one of the Writers' Guides. In other words, it tells the writers what they can and cannot do on screen.
First, see another answer where I posted another excerpt from the same section. That part points out that the molecules from a person or object being transported are stored in the pattern buffer, then we have this:
On page 29, under The Transporter - Once and for All:
From the Pattern Buffer, the molecular stream and the coded instructions pass through a number of subsystems before reaching the emitter. These include the Subspace, Doppler, and Heisenberg Compensators. Each works to insure that the matter stream is being transmitted or received is in the correct phase, frequency, and so on. (sic)
So when they're transporting a person or object, they are actually sending the molecules from one place to another. It's not just a radio signal, it's a stream of molecules traveling (in the annular confinement beam).
The shields stop transport because the matter itself, the stream of molecules, cannot pass through the shield.
(If you need more on this, there's a few more bits addressing the transmission transmission of the matter in the guide.)