The 'conventional wisdom' (pun intended), is that the syns had a) detergents or other compounds that dissolved deposits that were preventing leakage, and b) that the syns were so 'slippery' that our old-school gaskets and seals couldn't contain them. When I put Redline MT-90 in my gearbox and OD it did leak more--as measured on the dipstick and my garage floor--which I attributed to 'slipperyness' (there's a scientific term I'm sure). In most other ways, a synthetic is superior to a dino oil, but unless you are really punishing your oil it's cheaper/better to use a good dino and change it more often (the main advantage of synthetics is extended oil changes, which is not really useful in lightly-driven classics, whose oil should be changed at least once a year or more regardless of mileage). There is no credible 'incompatibility' that I've heard of.
There was an incident in the aviation community, however. Many years ago Mobil--leveraging their success with Mobil 1--produced Mobil 1 for piston-engined aircraft (IIRC, it was called 'Mobil 1AV' or similar). There were claims--not sure if they were validated by scientific testing or not--that the full synthetic did not do as good a job of scavenging lead residue as dino oil. This caused lead deposits to gunk up the rings, esp. in large-displacement Continental engines. Mobil bought some owners a rebuild or new engine, and pulled Mobil 1AV off the shelf (of course, lead buildup is not an issue in our engines any more). Last I checked--it's been several years--Shell was selling Aeroshell 15W-50, which is a dino/syn blend--best/worst of both worlds?--and Ford calls for their own 5W-20 dino/syn blend in my Mustang (which I've used religiously).
Long story short, if you've got a modern, tight engine use a full-syn and change it out every 10-15K miles. If not, unless you're rich--we all know Healey owners are rich (or were before we bought Healeys)--use any good dino oil or blend and change it out at least once/year, even if the car has been sitting. Syn's a better oil, but even with a modern additive package blowby will contaminate it quicker and you still need to change it (relatively) often.
Also, have heard that some newer 'synthetics' actually use highly-refined mineral oil as a base stock.