As a green card holder, I’d like to live and work abroad for several years, then return to the US. Is this feasible and how strictly enforced are the re-entry permit requirements in practice?
Yes, definitely and reentry permits are easy to prepare and generally issued without issue. You just need to be physically present in the U.S. when you file and again when you renew (if you renew) and also you need to get fingerprinted in the U.S. after you file (usually within a few weeks of filing).
