I still doubt you know what the problem actually is? Those LCDs are extremely stable, if your 5v to the display is stable. The data in the LCD can only change (be written) when you have the E line high, and since the E line is a PIC output pin and is low impedance (and you have a pulldown resistor and cap on E line) and your PIC holds the E line low at all times (unless writing) then there is another reason the LCD is getting bad data.
I would look at the 5v PSU rail, which s why I asked how you are decoupling the PIC and LCD 5v power from the rest of the equipment, a schematic would help a lot.
Then if the 5v is very good, and if you are sure the PIC is not resetting or brownout glitching etc, it becomes very likely there is a software issue. You should show your LCD code which shows the order you operate E,RS,RW etc and the time delays you are using.
It's also possible you have an actual bug in software that is simply writing trash characters to the LCD, and you thought it was a noise issue.