From my experience, LM3xx regulators are not at all that sensitive to ESR of output caps. In several dozens of overhauled CD players and preamp sections, I have never had any problems with low ESR (not ultra-low ESR, though) after LM regulators.
Read this paper, page 13 illustrates how to make an LM317 with insufficient phase margin when a tantalum is used instead of aluminum electrolytic:
http://www.omicron-lab.com/fileadmi...notes/App_Note_Noninvasive_Stability_V1_2.pdf
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