Connecting strain gauge output terminals to an instrumentaiton amplifier
I design strain gauge amplifiers and use a fair amount of gain and my observations are that imbalances in the bridge resistors are the biggest source of error. Having said that I go for amps that have good CMRR because the gauges are wired up to 10m distant and can pick up a fair amount iof noise. I don't use anything in between the bridge and IA.

If you're using quarter bridge active devices, as per your diagram I use constant current feed for excitation because it's twice as linear ie fewer theoretical errors.

I also use auto balance mechanisms on the REF pin of the IA fed from a DAC.