An XOR is a product detector, so you will have built a correlation receiver that will detect cross channel interference. Where can I find Cosmic Microwave Background free from interference? Would it not be better to throw out the dishes and just terminate the antenna leads in hot resistors with Johnson noise?− so far, no competent math or science guy or gal to whom I've described the notion has to me decried the idea as in any way not ok.
What are the “SETI filters”? Presumably you take raw data and remove signals, effectively maximising entropy of the data set. The result will not have recognisable patterns, but it will contain patterns you did not consider in the filters. In effect, you are reading the tea leaves.
That ignores the fact that real random noise contains short sequences of recognisable patterns. If you remove those patterns you have coloured the data, and the result is guaranteed NOT random.
For all we know, extraterrestrials maximise channel utilisation and correct all errors by communicating efficiently in what we see as random noise.