The play Medea wins our sympathy for its monstrous central figure. To what extent is this true?

There are three components in the statement that can be evaluated. The extent to which any element or the entire statement is “true,” however, is open to debate, as the statement calls for an opinion, albeit one based on evidence.
One component relates to the characterization of Medea as “monstrous.” This adjective seems to require a moral and ethical evaluation. While Euripides clearly shows that Medea kills her children, it is for the viewer or reader to decide if those actions make her a monster.
A second important element of the statement is that the play generates “sympathy” for Medea. This seems to contradict the “monstrous” element. Why would the viewer feel “sympathy” for a murderer? One could identify specific places where Euripides shows positive aspects of her personality or behavior. One example could be her aiding Jason to gain his freedom. Conversely, one could identify situations in which she made difficult choices from within a narrow range of options, or circumstances entirely out of her control, when she may have been victimized by another character. The latter applies especially to Jason’s abandonment. More generally, in the Greek worldview, destiny and the gods’ will played a large role in deciding outcomes, so sympathy might be influenced by accepting that element of Euripides’ presentation. Medea’s rescue by Helios might be a factor.
The third component is whether the play “wins” the viewer’s sympathy. If the viewer does feel sympathy, what elements of Euripides’ text influence that to happen? “Win” can also imply that at the play’s beginning, the viewer feels differently but is then persuaded to have sympathy. Does the audience’s view of Medea change from worse to better during the course of the play? That interpretation would depend heavily on the play’s construction.

At first, we are very sympathetic towards Medea over the callous way that Jason's treated her. She's a wronged woman, seduced and abandoned by a man for whom she took such enormous risks. Having been unceremoniously dumped by Jason, Medea is a woman all alone in the world, stuck in an unfamiliar city without any kind of support network. Worse still, she can't return home to Colchis, not after she brazenly defied her father and helped Jason escape with the golden fleece. Jason's abandonment has effectively reduced Medea to the status of a non-person. In ancient Greece, an individual's identity was bound up with their family and their city, and as Medea has been robbed of both she no longer enjoys any meaningful status in society.
Under the circumstances, it's perfectly natural for the audience to feel sympathy for Medea; she has nowhere to go in life. But there can be no sympathy whatsoever for the brutal, bloody way she goes about wreaking vengeance on the man she thought was the love of her life.