If an astronomer picks up a radio signal it is extremely obvious whether it is an artificial source or not. Natural sources have very inefficient spectra of very specific types. Artificial sources have very clear frequency cutoffs, having come from an antenna. Even frequency-hopping sources may jump around in a way that makes eavesdropping difficult, but if you stick around long enough on a single channel (as radio astronomers do) you'll get little blips now and then as the signal hops through your channel and is gone again.

How do we know this? Because astronomers see these every single night and have developed sophisticated filters to remove them. But by checking how the source is moving it is quite easy to tell if source is local or not, and sure enough all these artificial sources come from satellites, the troposphere, or an unshielded microwave.

It is actually remarkably difficult and a challenging problem in itself to create a communication mechanism which looks like a natural source. It defies imagination to think that every single intelligent species out there has purposefully masked their existence in such a way, including giving up useful technology like ground control radar or mobile communications.

The reason they have to filter out artificial sources, and the only reason they're a problem, is we are literally right on top of the source. These aren't even as far away as, say, Mars. New Horizons, for example, can't communicate with Earth unless it points its transmitter / receiver directly at us. And that's in our own solar system! Only a few light hours away.

Just think about it. The signals are going to be so weak by the time the photons get here they will be indistinguishable from the CMB.