Protecting Servers from Dust

In this situation, I'd tend to go the cheap/easy route - head to your local home improvement store and pickup a couple cheapo furnace filters. Then fasten them somehow (bungee cords?) to the front of your server rack. If you're unable to get a good "seal" between the filters or around the edges, just seal it up with packaging tape.

The filters will restrict airflow a bit, but it shouldn't be so much as to cause a problem.

(I have to credit Alton Brown's Beef Jerky recipe for the inspiration to use furnace filters in an unconventional way)

Make sure plastic sheeting is put up around all the doorways where the work is being done.

Make sure the server room door stays shut as much as possible. If there is a large gap under or around the door install some weatherproofing trim (which is good for keeping the AC in anyways).

Assuming the room has a drop ceiling make sure all the tiles are fully seated and seal up any holes with plastic sheeting and tape.

Have a vacuum handy to suck up the dust carried around on people's shoes, so it doesn't get tracked into the room.

Is the AC recirculating air or sucking it in from outside? If it sucks air from outside put the fan on max to try to increase the air pressure in the room a little. Make sure it doesn't suck air in from inside the building where it might pull in drywall dust.