I've always thought that the strength of the ILF is in its diplomacy - on the friends and allies it can call on if some filth pirates decide to wardec. Valkyr was the latest example, but DAMARCARES when the militias temp blued to protect the ILF tower was pretty special also. I guess Saxon has a number of admirers out there.
To be fair, you do have something of an advantage. The Intaki are pretty well liked and they're "rebelling" against a group of people that aren't so well liked (the Federation).
The Amarr are neither well liked, nor are they rebelling against a greater enemy. They are the enemy to most people. Heck, I've seen enough people say that the Empire is Public Enemy One even moreso than Sansha or any of the other threats in the cluster.
The ILF having been around for a very long time is pretty key, more so than any perception of the Federation, imo. New groups will usually struggle with this at first unless they get a kickstart via older, better-known individuals and organizations, either via out of corp support or people joining them. It's part of the growing pains of a corp, and something that can be rode out with time.
As far as people saying the Amarr are PE#1 over the toasters (or most other groups)? Laugh at them, then call them idiots while patting them on their adorable little heads. Because that amount of stupid is kinda cute, in a way.