Something tells me this is a easiest path versus a have to. You should be able to tell your computer to allow you to connect to whatever you need to without taking down a firewall. Firewalls aren't meant to block everything (well not all at least) but to keep out things deemed unwanted or unsafe. However since its a work at home job you can't be sure everyone is inelligent enough to configure their computer and it is just easier to tell people to take down their firewall.
Personally unless it paid enough to purchase a cheap computer just for that job I wouldn't risk it. All it takes is one thing, anti-virus or not and your whole system could be compromised. I haven't seen a work at home job I could work through a company that paid well enough for that yet though.