Can you do a masters in psychology without an honours in psychology?

It has been and can be done. In Canada, there are a very small amount of programs that still accept students without an honours degree. However, keep in mind that most students who continue to graduate school have honours degrees. At one point in time it was a leg up on the competition. Today its standard procedure and most universities require it. These days the leg up comes from publications which require you to actually conduct a study and write a paper, which is what an honours thesis is.

Further, there are very few terminal masters degree programs these days. Most often if you see somebody with a masters as their highest degree they were kicked from their program.