I am new to having a well and the pressure in our house is OK, but not incredible. The well sits about 100 ft. from the house. We have 2 20 Gallon pressure tanks next to the pump. The pressure switch is a 40/60. The pressure reads about 43 psi. I am curious if I can set the pressure higher or if I risk damaging the system. The majority of the plumbing in the house is PEX.
You can, but it's not all to the good...
Normally, most household plumbing fixtures (especially toilet valves) prefer a pressure of no more than 80 PSI. Your pipes are nearly always not the limiting factor. Most well pump controllers have a fixed 20PSI swing from on to off, but many can be adjusted so they can swing 40-60, 50-70, 60-80, 30-50, 23.5-43.5 etc.
The volume of water stored in your pressure tanks becomes less as the pressure is raised - a captive air tank swinging from 40 to 20 PSI stores far more water than one swinging from 80 to 60 PSI. This matters because more pump starts is one of the factors that leads eventually to pump death and replacement, always a fun time. So if you raise the system pressure, you should probably also increase your storage tank volume to prevent having lots of very short pump cycles. Switching over to a "constant pressure" (or "nearly constant pressure") system is another alternative, though it can be costly.
If you change system pressure, you need to change precharge air pressure in captive air tanks (typically about 2-3 PSI less than the lower cut-in pressure - ie, 58 lb for an 80-60 setting.)
You should observe system pressure as water is used - a properly functioning 40-60 PSI system should drop to about 40, switch on the pump and raise to 60, switch off the pump and drop to 40 as water is used. When no water is used the system pressure should hold steady. If you turn off all other water use and measure exactly how much water is needed to drop from 60 to 40 you can gauge the health and current storage capacity of your pressure tanks. If you measure the time it takes to refill from 40-60 (without drawing any more water) you will know your pumping rate (and if it takes less than a minute, conventional wisdom is that you already need more storage capacity.)
It is important to know where the pressure SWITCH is, as that is what is controlling your pressure.
You didn't say where your pressure switch is or what the elevation of the house and switch is. I'm assuming (usually a bad thing) that the switch is near the tanks based on the picture, but the house could be higher than the switch.
Water pressure changes by 0.433 psi per foot of elevation, so if your switch is 20 feet lower than the house, then at the low end of the 40 - 60 range (40) you will only have 40 - (20 * .433) = 31.34 psi at the house instead of the 40 psi you are expecting.
Let the system build up pressure and then measure the static water pressure (no water being used and pump off) at the switch or well (hopefully you have a spigot there) and at the house. Check for any differential and factor that into your pressure calculation when adjusting your pressure.
You said the well and tanks are about 100 feet from the house so you can also have a pressure drop due to the distance of piping and size of pipe used - only when the water is being used, statically you will not see this. Using 2" pipe * 100 feet @ 18 GPM = about a .3 psi drop.
So for this reason, you typically want the tanks and the pressure switch to be near the house NOT the well (my well is 150 feet LOWER than my house). If the switch and the house are about level and they used 2" pipes, then it probably doesn't matter much if the tanks are at the well or the house.
Otherwise, what Ecnerwal said.