Why am I being forced to pay an additional $20 for a "maximum refund guarantee" before I'm able to file?

Based on the screen shot you posted, it doesn't apperar to me you're being "forced" to do anything. Just click the Continue button, and do not click any other button on that screen.

If you have not yet filed : 

How to see your fees
https://ttlc.intuit.com/questions/2565973-how-do-i-review-my-fees-in-turbotax-online   

For help with fees 
https://ttlc.intuit.com/questions/1901213-what-can-i-do-to-reduce-my-fees   

The screen after I press "continue" takes me to a payment screen with no option to skip.

The screen after I press "continue" takes me to a payment screen with no option to skip.

Correct. You have to pay for the use of the program, before you can e-file your tax return. If you're filing a state return you also have to pay for the state module, as well as another separate fee to e-file the state return.

If you are using the DOWNLOADED/CD program then there is a $20 fee to efile the state return  on top of the fee you paid for the program to start with.   You can avoid the fee by backing up and choosing to mail in the state return instead of efiling it.