Strike Ends (Maybe) at Brandon University. Are Profs "Essential"?

This may come as a surprise to many outside of Manitoba, but there was a faculty strike that shut down Brandon University for over a month, locking some 3000 students out of classes.  The strike ended tentatively last Friday when a deal was reached between the union and employer.  This was the longest work stoppage ever at a Manitoba university at 45 days. The strike here at York in 1997 lasted 55 days.
Last week, the Manitoba NDP government used its statutory power to order the professors to vote on the employer’s last offer. However, a tentative deal was reached before that vote took place.  Now the faculty will vote on the proposed deal, suggesting that the government’s move provoked the parties to find their own settlement. In a somewhat unusual move, classes appear to be starting today (Monday), even though the union members won’t finish voting on the deal until the weekend.  What if they reject the settlement?  I guess the strike would start up again.  No details about the tentative deal have been released.
As usual, there are calls by students (and their parents) to “sue” the professors for engaging in a lawful strike, and for the government to declare university professors “essential” so that they cannot strike at all.
What do you think?

Should professors like me be entitled to strike if we do not like how our employer is treating us, or if we think a strike will allow us to win a better employment contract?
Or should we add professors to the growing list of workers who should not have a right to strike?