Older crankset and newer 7 speed rear cog.
Crank set is Campagnolo Gran Sport.

I set the frame from 120mm to 130mm.
The small crank ring is too close to the outer ring and when the chain is on
the small chain ring and in 7th gear, the chain rubs the backside of the outer chain ring.

Is it normal to space out the crank set inner chainring for more clearance?

No.
It's normal to not use that gear because it's cross chaining.

A seven-sprocket cluster is wider than a five-sprocket cluster, so the chain angle is greater when you use the extreme gears (i.e. large front ring/largest rear sprocket or small front ring/smallest rear sprocket); this can cause the chain to rub the outer ring when on the small/small combination. This is exacerbated by short chainstays and/or a large difference in chainring tooth counts. The fix is to avoid using those extreme gear combinations, which is considered to be Good Practice in any case.

N.B. you could in principle use spacers under the bottom bracket fixed cup to move the crank further out, but this can create its own problems with chainline and front derailleur reach.

The newness of the 7 speed rear cogs is immaterial. 7 speed spacing is 7 speed spacing no matter the vintage. What is more important is chainline and the relative size of your front chainrings. In general, the larger the difference in size of your large and small chainrings, the more likely it is that your chain will fall into the "shadow" when you use your smallest rear cog in combination with your small chainring. Short chainstays exacerbate this problem. Question: what size chainrings on your crankset?

52/42

This. The small-small gear is the least efficient one possible, and there should be an equivalent gear (or close) on the big ring that will run smoother anyway.

So, one less tooth to pull. Chain line and chainstay length are next. How long are your chainstays? Short ones are prone to causing the problem you are seeing
Or, maybe just provide full information about your bike, could save a ton of back and forth

Not short. It's a 79 Raleigh competition GS.