Conjunctivitis is contagious to other birds. I'd recommend taking the feeder down and washing it thoroughly in hot soapy water, rinse with water, then rinse the feeder w/ a bleach solution (1 part bleach and 9 parts water), and let dry completely. Rake up any old seed under the feeder and dispose in the trash. Try to wash the feeder at least weekly. If you have many feeders, try spacing them out so that the birds have room to spread out. For the house finch, just keep providing clean food and seed at the feeder.