I was an apartment manager for about two years. This is what I would figure is going on here.
The apartment manager rarely acts on his/her own. The owner is probably the one behind this, so don't even bother trying to go over their head.
The reason they are bugging you is because the rack isn't a permanent fixture of your vehicle, and peds and such do not expect it to be there. It would be similar to carrying a ladder in the back of a pickup truck. They, unfortunatley, can make up stupid rules like this. most likely because someone else in the complex complained about it. You may try asking if covering the rack with a bright fabric or cones or something, to draw attention to it, would be acceptable. Anything that makes it stand out may be OK with the management.
Unless they're jag-offs
burbanbiker, in Illinois, if they did that to you, you would have a lovely lawsuit to file. Making reasonable accomodation to a resident that is NOT affected by any kind of handicap (ie wheelchair access, etc), and not allowing for the same accomodation for any other resdient is considered discrimmination here. I'm surprised it's allowed in California.
BTW, I quit my manager job 3 years ago because I hated the politics of it all. But meeting the new residents was pretty cool.