Rocket exhaust is bright in visible light, we can still see through it but when there's hot, glowing soot it's so bright that we think it's opaque, but it's not. See answers to How does the camera make the exhaust of the Electron's RP-1/LOX exhaust transparent?
But radio is much lower frequency than light and if there is ionization present in exhaust then the plasma frequency associated with the electrons might be high enough to attenuate or otherwise interact with radio transmissions between a spacecraft and something else.
You can convince yourself that flames have ionization by watching the videos below and reading the One Tube Radio blogpost Flame Speaker Science Fair Project but this doesn't necessarily mean that the electron density is high enough to become opaque to RF.
Question: Is there any information at all that describes and quantifies the radio opacity of rocket exhaust? Has this (or related interactions) ever been discussed in detail or even measured in the context of spaceflight?
The two embedded videos below illustrate the plasma component of a flame by applying a high voltage to a flame and accelerating the ions in the flame, which are heavy enough to make sound by transferring their motion to other molecules as well. People also make diodes and triodes from flames and use them to rectify and/or amplify radio signals and these frequencies require the participation of the lighter electrons; see for example these videos: