You don’t have to train and apply ICA to data with identical high-pass filters. It is strongly recommended to train ICA with data that has been high-pass filtered at 1Hz or even 2Hz, but you can then apply that ICA solution to the same or other data sets that have different or no high-pass filters at all.
Regarding the low-pass filter, I don’t think that it is critical to apply a low-pass filter before training the ICA. Usually, I don’t apply a low-pass at all, because filters can have dramatic effects on large spikes or other artifacts, and I’ve found ICA to work quite well without any low-pass filters (of course you already have a natural low-pass filter that was set during recording with a cutoff frequency at the Nyquist frequency or usually much lower).
The EEGLAB tutorial has some nice suggestions on how to optimize ICA quality, and they only talk about how the high-pass filter is very important and don’t even mention the low-pass filter: d. Indep. Comp. Analysis - EEGLAB Wiki