I don't see any danger in removing them for liftOver (indeed it may be necessary to do it). They might be of interest in some rare cases such as evaluation of mapping software, characterizing multimapping reads etc - but as for myself, I have never really used them.
it really depends on what your bed file is used for. for instance, we use them to define regions of interest, which are used for defining the sequencing experiment and also through the downstream analysis to focus in particular regions of our bam alignments and perform operations on such particular loci. although we may end up after alignment with reads that would have aligned to chrUn* or chr*_random, since the knowledge we aim to obtain is not to be contained on such contigs, we do not consider them when ultimately reporting variants or coverage. we still leave those reads on the bam file in case a new aligner is able to position them somewhere else, or if any particular experiment would be interested in looking to that contigs in particular, but since this is not the daily usage that's the main reason why we never include them in our experiment designs' bed files.