I wouldn't say "barriers" so much as challenges she's definitely going to have to deal with more than your typical T1D patient. I don't think they'll impact her ability to do her job, but I do think her job could make taking care of herself more challenging.
Given how much stress can interfere with blood sugar control, she's in for a doozy whilst dealing with the chaos of the Brexit situation.
I know I've seen a lot of people talk about having problems with blood sugar control when traveling due to having to change the timing of their insulin doses. The job of PM may require even more travel than she's already engaged in, possibly across more timezones than she has in the past on a more frequent basis.
Politics, and being Prime Minister will also likely mean more social events and meals, often at non-standard times from her "usual" schedule (if she's even able to keep any sort of "usual" schedule" with the long, unpredictable hours the job may require), and often catered with no choice in what she's given to eat, I'd wager.
I don't think anyone is saying she can't, or shouldn't do the job (yet). The article even specifically said that so far no one has made an issue of it. The article specifically states that she has a good reputation, and has made a good impression. Like rgcainmd said, her having T1D doesn't really have anything to do with her being Prime Minister.
Something to keep in mind is context and audience: the article is on insulinnation.com - it's written for an audience of other T1D patients who may be interested in the accomplishments of other T1Ds. A blog that focuses on T1D wouldn't write about this woman if she DIDN'T have T1D as general politics doesn't seem to be part of their usual content.