By coincidence, I've just been identifying some antenna socket hash from the RSPdx when operating on 2200 m (136 kHz). I was feeding the RSPdx via a splitter internal to my TS-890S and, while there is no direct pickup of hash by the transceiver, enabling the Kenwood's antenna (passive) splitting function results in digital system noise which is audible and visible on the bandscope. I haven't looked for noise on other bands but, on the face of it, if you're splitting an antenna output between an RSPdx and other receivers, a distribution amplifier with decent isolation makes sense. As an aside, if you're interested in the new extremely narrow bandwidth FST4 modes on the low bands you'll likely also need an external reference source since the RSPdx internal reference is not stable enough for the long-duration modes.
For the OP, and perhaps to use alongside some of the suggestions so far, you could also consider a cascaded receiver protection system incorporating something like the Array Solutions front-end protector (
https://www.arraysolutions.com/as-rxfep), or a homebrew equivalent. The saturable transformers work very well in practice.
73, Peter.