Most "new" parts will fit (if we're talking 70's-80's bmx cruiser parts.)
I have Araya 7x alloys (26x1.75) and 26x2.3 kenda krad tires on my 48 DX, with a german Durex 135mm coaster brake. Tires fit fine, had to spread the chainstays for the hub (yanked 'em apart by hand,) but everything is straight.
Fenders and chainguard, though, that's another story.
I figure the main reasons klunkers (then and now) didn't run them, was because fenders are heavy, you'll get chunks of mud stuck in them, you'll tweak them when you crash, and changing flats would be a hassle.
Same goes for chainguards. It'll break off, you're cranks don't fit, it'll bend into the chain and sprocket when you crash, and putting your chain back on would be a hassle.
Plus, they (we,) just go for the bare bones necessities. Riding uphill with and added 15lbs is no fun, and carrying broken parts down a mountain would suck, too.