Can Blue Shield cancel your insurance if you get sick and have an operation within the first 30 days of coverage?

Insurance cannot cancel people anymore under Obamacare rules for the reason you gave, that you used the insurance coverage within the first month. Assuming you were paid up.

They can't cancel it just for the reasons that you gave. Of course, if there is another reason why they can cancel, then they can cancel.

They can cancel you if you don't pay. It's been that way for many, many years.