Currently when the beginning of a sentence is in quotes, the first letter is not capitalized.
"for example, the f at the beginning of this sentence in Libre writer would not be capitalized."
Operating System: Windows 7
Version: 22.214.171.124 release
issue confirmed with 126.96.36.199 under Win7x64
the same problem affects OOo, old LibO releases and AOO 4.1 so the bug is inherited from OOo.
I think the problem is that when you apply "first letter capitalization" the quotation mark or any othe symbol is seen as the first letter that's why the f letter is not capitalized because it's actually the second letter.
this is a duplicate of Bug 63432, doesn't matter if first letter capitalization is applied during typing or with the format menu item
*** This bug has been marked as a duplicate of bug 63432 ***