To answer your specific question about connecting the LFR DSP between your receiver pre-outs and your amplifier, you absolutely want to stay with the same connection type both in and out. The reason for this is that the DSP has a fixed gain of unity or 1:1. It does not apply any gain to the signal path. This is fine if you maintain the same input and output connection, but if you were to use the RCA inputs and then connect to your amplifier using XLRs, the overall gain of the DSP would now be -6dB. If your amplifier requires more than 2Vrms in to reach full power, you would then clip the input of the DSP before reaching your maximum amplifier output which is a bad situation. That's why we always recommend staying with like connections.
For the broader question about XLR connections in general, I have found them to be beneficial between pre-amp and power amp if the amplifier is situated more than 6 feet away from the pre-amp. A true balanced connection can also help if you live in an RFI rich environment (near a radio or cell tower) and also gives some benefits in terms of reducing the background noise floor and residual hum due to ground loops.
So this isn't a dumb question at all! In fact, now I need to ask a follow-up question based on my own setup. In it, I've used XLR outputs from my pre-pro to the DSP. Then I've used XLR outs for Left and Right (both front and rear) from the DSP to my ADA for the LFRs. However, I'm using an older amp for my centre and surrounds and it doesn't have XLR inputs. Thus I've run an RCA out from the DSP to the input of the amp for the centre.
I haven't noticed any issues yet but is this also reducing the gain of the DSP? Should I switch to all RCA for my centre channel?