Say an LCD laptop / cell phone / monitor screen got shattered.
Are the liquid crystals toxic? Do they vaporize? Are harmful to eyes if they touch the eyes, or if inhaled (evaporation?)
What are the LCD contents made of exactly?
Wikipedia has everything you want to know.
The bottom line is LCDs are pretty safe.
The real hazard is the sharp edges of the broken plastic. Since you want to avoid those, you will automatically be avoiding the materials inside anyway.
Some older laptop screens had fluorescent bulbs to provide the backlighting. If those broke open you could be exposed to Mercury vapors. But LEDs for backlighting have been the norm for a long time.