If the diode "burns" (melts) easily the goggles (as black plastic of the same kind), then they absorb well it's wavelength.
I have $3 red goggles which i tested on a 405nm Sony SLD3235FV diode sold on ebay.
I have accidentally pointed the diode into my eyes through the goggles. I saw it like emitting tiny red spot despite it's an UV diode. When I look at reflected from non-fluorescent material beam, I can not see it.
My eyes did not get hurt, but I wasn't running the diode at it's full power. Actually it was 5 promiles PWM at 90mA, because I needed to look at the spot to focus it and it shoud not burn the matte plastic I used to focus at.
5 promiles = 0.005% ( Fpwm=2kHz, Tpwm=2000, Ton = 10 ).