Updating my vintage Shimano 600 chain rings Will the chain rings support the new 7 speed chain? the new one will actually be new old stock: Shimano 600, 1983

I'm putting on a new 7 speed freewheel, chain and rear derailleur.
There are a couple different approaches. You can select basic, traditional-style chainrings similar to what came on it that don't have any shift-assisting ramps or pins, or you can put fancier indexed-shifting-friendly rings on it.

Traditional plain rings are often sold under house-brand type names such as Vuelta, Origin8, Dimension, etc. They're often fairly cheap, although fancier ones in this camp do exist, i.e. the laser-cut-in-the-US Salsa ones that were around for many years, or something like T.A. rings.

These sorts of rings are more or less designed to replace stock ones on older cranks such as Shimano 600s. They'll probably just work with a 7-speed chain with no issues and no need to mess with anything.

If you wanted to get ramped and pinned rings, which are more designed with 9/10/11-speed era chains in mind, you may run into issues with them being intended for narrower spacing, which may cause issues such as the chain wanting to rub on the large chainring when in many small ring combinations. Chain compatibility issues in this direction can almost always be solved by tuning the spacing with chainring shim spacers, such as the .6mm Wheels Mfg ones or a small stack of the .2mm FSA ones. And on that note, you may find you need them on the other setup too; chainring spacers are always handy to have when replacing chainrings. They're kind of the way to make things work when the "right" chainrings are no longer available or whenever you're using a chain type that's wider (aka older) than the one intended for the cranks or the rings.