I got a package of 32 Degrees t-shirts at Costco that aren’t too bad. I’m planning to try the next size up to see if a little looser fit helps even more with the sheer factor.
I used the search engine and it came up with one white top by llbean and another by madewell. I’m currently at a mall and haven’t seen anything, including some of the stores mentioned here in this thread. All are pretty thin, even Nordstrom’s, Ann Taylor and others.
I have had good luck with Calvin Klein brand blouses and lightweight summer sweaters from Talbots, Loft, Land’s End, etc. Best to catch them on sale though.
Not cheap, but Brooks Brothers blouses are nice and opaque. Especially the no-iron ones.
I got this one recently. Not on sale, but it was the last one in my size in inventory at the moment, so I pulled the plug (it made me think about this thread):
https://m.shop.nordstrom.com/s/nordstrom-signature-lace-up-eyelet-top/4844990
Quite a few cute white tops by the same Nordie’s house brand!
Linen is great for heat and never transparent.
Chico’s has great blouses, crisp no-iron cotton, that aren’t see-through. They also make, or made, a linen blouse with 3/4 sleeves in a number of luscious colors.
I have both in various colors. Would be good for office wear, too, especially the cotton.
Chicos does have things that aren’t animal prints, heavily patterned, or sequinned. 
I’ve bought a number of nice, plain items in natural fibers from them.
Our local Assistance League has a great thrift shop. They have a Boutique section that is 1/2
off first Friday of month. I bought two great white tops $4 each. One a loose cotton crochet and the other a thin rayon. I work in a place with lots of AC. I have a nude color cami that make the tops appropriate when I work at the more conservative position.