Karsten99: Can a human, half-elf or elf woman reach strength 20?
Answering curtly: No.
Karsten99: Or are they capped at 19 due to their gender penalty?
Female humans and half-elves are capped at 19. Female elves are capped at 18. Elves of both sexes have an extra point taken down from the start and to their cap, when compared to the "standard" (humans).
Karsten99: From what I've been reading there seems to be differing opinions
There is no place for opinion in this matter. Someone is either right or wrong when answering the questions you asked here.
Karsten99: (...) can you take a "no significant background"" character all the way up to 20?
No character that starts with a stat at less than 8 (before assigning the initial 5 points) can reach 20 in that particular stat. It does not matter if it is because of race, sex, or background.
And as many points less that they have below 8, the same points below 20 will be their cap.
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Knowing all of the above, a more important question would then be: can all characters that start with more than 8 in a stat reach over 20 for that stat?
The answer is "No, only some can".
For example: Elves with "No significant background" can reach 21 DX, BE and WP; but a male human with the "Apprenticed to a blacksmith" background cannot reach ST 21 (only 20).
In the particular case of your concerns (female humans, elves and half-elves, with "No significant background") all work as expected from the starting stats that they have, with the exception of the humans' CN, which can only reach 20, instead of the expected 21.
In my opinion all these "not being able to reach N stat, despite the starting bonus" was not intended by the devs, and I find it strange that it has not been addressed by the UAP in any of its iterations. But I have not kept up with the discussions of the modding scene, and maybe there is a reason for that to have been left as it was in the original game.
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Sources: My own previous experience with both the original release and the previous UAPs; and also by trying out characters now with both an unmodified GOG game and with UAP 1.5.1, adding the Virgil Debug mod to speed up the tests. There are plenty of people more experienced at Arcanum than I am that visit this forum regularly. To them: if I made any mistakes or omitted anything of importance, please let me know.