Is there a way to get my Android report to my cell phone company that it's not a smart phone? I have a phone, but it doesn't need internet (I use it as a regular phone + wifi). However, the cell phone company decided that if I have a smartphone, it needs to come with a data plan.

Can I do anything (including modify my rom) to look like a regular flip phone to my carrier?

I have a sim-card phone.
As far as I know, phones don't report to the carrier if they are smartphones or not. They only report their unique IMEI number, from which they can't tell the type of your phone. (Unless they ask the manufacturer.) Also it is illegal to change. The carrier forcing you to pay for a data plan simply because you have a smartphone would be weird and highly unacceptable.

What I think is happening here is that your carrier has a "default data plan" with no subscription fee and a high rate, which is available to all customers by default. Your old "dumbphone" didn't use it, so you didn't get billed for it. Your new smartphone, however, uses it by default when it isn't connected to WiFi, so you get billed for it. (My old carrier did this with the price of $0.05 per 10kB, restarted at every connection to the mobile data. So every time I turned on my phone or moved out and back into coverage I got billed. I didn't even have a smartphone, just a semi-dumb one which could visit simple web pages. I was pissed when I found out.) The solution could be


Disabling mobile data in the settings
Asking your carrier to disable this default data plan
Setting wrong APN names so that your phone isn't able to connect to the mobile data