I'm using a Win7 machine and Inkscape 1.0. I was trying to use 'NationalPark' in Inkscape (regular, heavy, outline, thin). It shows heavy fine, but it displays outline when it should be regular. I deleted the fonts and re-installed. Didn't work. I uninstalled and re-installed Inkscape with no luck. The works fine in Photoshop, so I know it isn't the font.

I can confirm on macOS - no idea what issue Inkscape has with it while other apps not.

(No big loss as its default kerning is somehow off.)

Inkscape conforms to CSS standards, so a number of fonts won't work as designed.

These fonts may have issues, as FontForge throws warnings:

That said, often fonts can be hacked to be in a different family, or in a standard CSS style. Below I renamed the "Preferred Family" in those fonts using FontForge.

So, I have access to the fonts in Inkscape, but there may be confusion if you use the fonts in other software, but probably ok.

More info on fonts & faces here:
http://tavmjong.free.fr/blog/?p=822

I am very careful with font installations - any warning macOS prompt and I will trash it. I got it from the official site - it´s vector drawing is excellent - the kerning not - but macOS Font.app idn´t throw any issue at me regarding the 4 fonts:

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You are welcome to try the fonts I have saved using the modified Preferred Family TTF info.

Wonder where you got the font from as mine are ".otf".

That is the display of the font info after I saved it as TTF. I downloaded the otf fonts the OP attached.

Here's FF's report on the OTF:

I ended up using an old version of Illustrator and converted them to outlines saved the file. Imported them into Inkscape.

The odd thing is when I deleted the fonts, Inkscape still showed them, even after I closed down Inkscape and restarted.

HikinMike

The odd thing is when I deleted the fonts, Inkscape still showed them, even after I closed down Inkscape and restarted.

Windows is funny sometimes with fonts.