In the case of loose Vf tolerance, one more spec should be considered, that is luminosity as a function of current. For example, I found a spec for a device which gives these values for relative luminous flux v. forward current:
.9 @ 300ma
.65 @ 250ma
.6 @ 200ma
So, for example, assuming nominal forward voltage drop of 2.5V, and max and min of 3.0V and 2.0V respectively, and assuming 5V supplies, we can easily determint the relative luminosities:
case 1: Vf=2.5V (nominal)
For I=250ma, R=2.5V/.250 = 10 ohms.
relative radiation = .65
Case 2: Vf=2.0V (minimum)
I=3V/10ohms=300ma
relative radiation = .9
case 3: Vf=3.0V (maximum)
I=2V/10ohms=200ma
relative radiation = .6
So, by designing for 'nominal' value of Vf, then using a device at the 'high' limit of Vf gives about 8% less radiation. That might or might not be acceptable. Also, for Vf at the 'low' limit gives a current that might or might not burn the LED.
If any of these limits are unacceptable, then you must either use a different LED, a different voltage or use a current driver.