CRTs put out very little UV, almost immeasurable, and not nearly not enough to harm you.
There are some fairly strict rules on the amount of UV radiation that is allowed; but the amount of UV is unmeasurable in CRTs for the reasons above.
CCFL LCDs don't put out a measurable amount of UV, and the CCFL bulbs are shielded to further prevent possible emissions. LED LCDs put out even less than CCFL (arguably none, depending the LED backlight type and the individual LED construction technique).
The XP Society attempted to measure UV that might be radiated from LCD screens. They were unable to detect any UVA or UVB using meters capable of measuring as low as 1 microwatt per square centimeter in the UVA and UVB spectrum.
Source: Xeroderma Pigmentosum Society, Inc.
...if any company sells a large UV protection plastic...
There's basically no such thing, as all plastic blocks UV. Even non-tinted ones:
The plain fact is that plastics are not very
transparent to UV light... Some plastics will pass some
near UV, ie. close to 330 nm, but UVA, B and C will not
pass. Tinting may not affect the UV transparency, but
clear plastic blocks UV just a good as green plastic.
My clear prescription glasses, plastic, block UV light
as good as dark sunglasses.
..
For fun we would take the light sensors outside and
measure the UV blocking of expensive vs cheap
sunglasses using students hanging on the "concrete
beach" at the student centre. Many students, were kind
of angry to find out that $5 plastic glasses blocked as
much UV A/B as $300 designer glasses from those fancy
shops in the upscale malls.
Source: Kenneth Mitton, Post-doc/Fellow, Molecular Development Retina, Cataract, Dept Ophthalmology / U. Mich