Why do some LCD manufacturers use linear polarizer and some others don't?
It seems to me that you have been shipped tinted film.
To test for linear polarized film rotate one piece in front of the other. When lined up as laid out in the original sheet they should pass light. When rotated at 90° they should block all light and appear black. (You obviously know this.)
To test for circular polarization:

The simplest test for whether a polarizing filter is really and truly a circular polarizer is very easy. Look through it into a mirror. [In one orientation] light is reflected off the mirror and passes back through. There is some darkening (about 1-2 [camera f-]stops with each pass through the filter). There is very little color cast visible.
Now reverse the filter. Now the mirror image of the filter is very dark.
If you try the same test with a good linear polarizer, there is absolutely no difference on reversing it - the image looks identical, and with minimal color cast.

Source: Beware cheap &quot;circular&quot; polarizers. Text in [ ] are my insertions for clarity as the article is about camera filters.