I have a trouble understanding why update ignore sql query would have an impact on replication? Could someone explain a way that I could understand instead of pointing out that it is unsafe for statement-based replication..
This is right on the help page for the UPDATE statement
UPDATE IGNORE statements, including those having an ORDER BY clause, are flagged as unsafe for statement-based replication. (This is because the order in which the rows are updated determines which rows are ignored.) With this change, such statements produce a warning in the log when using statement-based mode and are logged using the row-based format when using MIXED mode. (Bug #11758262, Bug #50439) See Section 188.8.131.52, “Determination of Safe and Unsafe Statements in Binary Logging”, for more information.
Seems clear to me -- what exactly is your question?