This is what www.theplantedtank.co.uk/algae.htm says about hair algae:
Description These are very general names for a wide variety of filamentous algae. Generally green and varying in length. I have listed some of the more popular filamentous algae under their own section on this page.
Cause A range of causes including low CO2, low nutrient levels and ammonia spikes. Nothing to do with excess iron as commonly thought.
Removal Can be very difficult to eradicate at times. A high plant mass with good CO2 and a good supply of nutrients along with constantly hassling the algae seems to pay off after a while. Removal by twisting around a toothbrush or similar. Overdosing Flourish Excel can help. Amano shrimps, Rosy barbs and mollies will often eat it.
Replacing everthing might help but if you don't deal with the root cause it may just come back on your new stuff. I would go for a really good scrubbing of everything, watch your water stats like a hawk, if possible invest in an "eater" of the algae, and maybe try the overdosing of liquid CO2 first before you buy a bunch of new stuff.