It has nothing to do with the first marriage being Religious or not. 2 of my brothers-in-law were told to get annulments in order for the marriages to be blessed. One did. The other - who was married in a civil ceremony, was not baptized, short marriage - would not and did not get an annulment. He and sis were married in a civil ceremony performed by a gay priest friend who was no longer actively ministering.
Canon law is odd to outsiders, but there it is. I don’t always agree with the rules - it can be easier for some people rather than others to get annulments w/o rhyme or reason. (The abusive ex of a family friend who got one and married again, for example.) It’s just one of the things to deal with when you want to marry in the Church.