I want to put a piece of grill cloth between my 3 inch port tube and the outside flange to keep my kids' little legos, fruit snacks, etc out of the speakers and because I think it looks good. Will this hinder air flow enough to impact the performance? Thanks.
Rather than use grill cloth, I would look for an open weave fabric. Grill cloth tends to be too finely woven for these purposes, and if your port is front firing, all you will see is it going in and out with the airflow. For a cool look thats blocks even less airflow, try using strips of fabric or other elastic material with a half inch spacing between them for a sort of vertical bar look, like the grills seen on some of the newer speakers. Just because sound waves travel through it doesn't mean air will, and this can alter the tuning of your speaker.
Restricting the flow from the port will decrease the efficiency of the port and will cause the port resonance peak be lowered in level. It may also cause the resonance frequency to be shifted slightly upward.
The over all result of this is that reproduced level of the lower frequencies will be decreased. The amount of the decrease can be controlled with the amount of restriction placed in or in front of the port. This is sometimes helpful in a system that is showing signs of to much bass on the low end, as may be caused when loudspeakers are placed close to the walls or corners of a room. It is possible to reduce the overall low frequency response at the very low end by 2 or 3 Db by varying the amount of restriction of the port.
A benefit of restricting the port is that the response time of the loudspeaker system will be faster near the effected frequencies. Thus it may give slightly better defined bass, although at a lower level. This is because the system is closer to the characteristics of a sealed enclosure.
It you wish to have the least effect on the very low frequncies then a method the provides minimum air restriction should be choosen.
People probably shouldn't get too fixated on one layer of single or double knit fabric having a significant impact with regard to port resistance.
A standard test for port resonances is doing a so called 'click test'. If this test indicates resonances, the 'cure' is adding successive layers of cloth to the port until the resonance disappears. In those situations where I've seen/heard this solution applied, the added cloth had no audible impact on the subs performance.