I am renting an apartment in Lawton, Oklahoma off post from Ft. Sill. 
The cable company that serves my apartment requires a $48/month TV
cable subscription (their extended package; not even the cheapest
offered) if I want to buy an internet access package as
well.  How do I get around this (I am not interested in a TV
subscription) because this feels very wrong in terms of legality
(monopoly abuse/forced purchase).  If it is legal, can I still
circumvent it?  If not, how do I prove it to the cable company?

Cable company website is http://www.lcisp.com

I would not say that this is a case of a monopoly because

1. They are not your only Internet option

-- you could have dialup or you could get satellite service, etc.

2. If you don't want to pay for the internet and cable, you don't have to. 

No one is forcing you to do anything.

Just don't sign up and you won't have to participate in their scheme.  

I would look into satellite services or any wireless services around
if they are the only cable internet option.

Have you checked to see if there is an ADSL option?

These are bringing broadband to lots of places here in the UK.

Call your telco.