This video is slightly misleading.http://axamonitor.com/doku.php?id=peters_kickstarter_facts
Alec Peters DID make some profit off of this in the form of the salary he gave himself. That is, by definition, making money off of someone else's intellectual property, which is illegal. While they are right that the restrictions Paramount put out on fan films are pretty extreme now, I think AXANAR does deserve a lawsuit. When you start making money off of a property you don't legally own is when you've crossed the line.
Legally own or have obtained rights to make a profit. Many propmakers who sell replica props do so because they have obtained the right to create and sell them for a profit. The IP holders often get the lion's share of the profits (some as high as 90%), as they should, but the individual makers do get some of it.
Now, if you are making a product and there is no profit being made from it, then you're legally in the clear. This is why the 501st, the Rebel Legion, and the Mandalorian Mercs are as big and popular as they are. Lucasfilm, and now Disney, doesn't have a legal leg to stand on with them because everything they do is 100% non-profit, and to top it all off, they are doing TONS of charity work, which looks good for Disney. It would be a PR Nightmare to go after them.
Now, what may save the guys at Axanar is if they are legally a non-profit organization with the appropriate tax benefits. This would allow them to pay the employees and leave no room for Paramount to go after them. However, if they are not an official non-profit, they're legally screwed.