Question

Why were Loyalists willing to support continued British rule but Patriots were not?

Answer 1

Loyalists weren't "afraid of change". This is propaganda, not reality. Loyalists disagreed with the patriots of many points ranging from taxation to the type of government they wanted to live under. Loyalists had the same courage of conviction the Patriots had, they simply saw the role of government differently.
Source:
http://www.redcoat.me.uk/