Do you agree that Barton has no choice but to let Marilyn die?

This is an interesting question from the vantage point of our modern sensibilities. Today, we live in the era of vast technological accomplishments. For example, we are experiencing the emergence and implementation of 5G now. Briefly, 5G is the new generation of wireless technology, set to revolutionize AR (augmented reality) and VR (virtual reality) applications in the business, healthcare, autonomous vehicle, and gaming industries.
We also have AI (artificial intelligence) and machine learning applications that are changing the way we protect sensitive consumer data and how we deliver accessibility in terms of customer service. So, in our modern era, we can't conceive of the kinds of limitations we read about in The Cold Equations.
Now, if we analyze the pilot's predicament based on the story's principles, it would be impossible to blame Barton for his difficult choice.

There could be no alternative. Additional fuel would be used during the hours of deceleration to compensate for the added mass of the stowaway, infinitesimal increments of fuel that would not be missed until the ship had almost reached its destination. Then, at some distance above the ground...the unmissed increments of fuel would make their absence known; the EDS would expend its last drops of fuel...Ship and pilot and stowaway would merge together upon impact as a wreckage of metal and plastic, flesh and blood, driven deep into the soil.

The following are some important questions to ask in order to arrive at an answer to your question:
1) Should Barton sacrifice himself, will Marilyn be able to pilot the EDS and reach the required destination safely?
2) Should Barton sacrifice himself?
3) Should Barton take a chance and keep Marilyn on the EDS ship, potentially sacrificing the lives of six other individuals?

Barton's confronted with a profound moral dilemma. If he allows Marilyn to remain on board ship, then he potentially jeopardizes his own safety as well as the success of what is essentially a mission of mercy. On the other hand, jettisoning Marilyn into space will lead to her certain death. The dilemma boils down to whether the individual is more important than the collective, or the wider community.
One could argue that Marilyn is being selfish in hitching a ride aboard the Emergency Dispatch Ship. The ship's carrying an essential cargo—desperately-needed medical supplies. Even if Marilyn thought that she'd only get off with a fine or a warning for stowing aboard ship, she must have known the ship's purpose and how important it was not to disrupt its vital mission. Tough situations require tough decisions, and although ejecting Marilyn into the icy wastes of deep space would be a tough decision indeed, it would also be justified under the circumstances.