Unlike Science, Religion does not need to offer predictions nor make falsifiable statements.
Nothing needs to do anything, but it's pretty clear that all significant religions do make falsifiable statements. Practically, any religion that doesn't have an effect on this world isn't worth much.
Some versions of all significant religions are making falsifiable statements. But making a falsifiable statement does not necessarily result in a conflict with science. Many religions are making falsifiable statements that are mostly likely true, such as: Building your house on rocky ground makes it safer from floods than building it on sand.(Matthew 7:24) There is only a problem if a statement is proven false, but people will continue believing it, because their religion says so. If a statement is found to be false, many religions will declare that they must have made a mistake in the interpretation of their holy book and change their interpretation.
Practically, any religion that doesn't have an effect on this world isn't worth much.
I agree, but Religion do not need falsifiable statements to have a effect on this world. Falsifiable statements can be falsified because they describe the world and these descriptions can be wrong. Empirical measurements can be used to show that a certain description of the world must be wrong, because it disagrees with measurable facts. Religions change the world by making statements about how the world should be and believers acting on these guidelines. But it is only possible to measure how the world currently is, not how it should be. Statements about how the world should be are always not falsifiable, but can be extremely powerful in changing the world. Science describes the world as it is, philosophy and religions try to make statements about how the world should be.
Science can make a statement like if we do X, Y will happen. That is a falsifiable statement that can be tested. It does not tell you to do X, it only describes the consequences of doing X. People still need to decide that they do want Y to happen, only then they can derive the statement that X should be done or not done. Deciding if X should be done, depends if you believe that Y would be good or not. Sure, for some Y nearly everyone agrees that this Y should be avoided, and the hard question is not "do you want Y to happen?" but "if you you do X will Y really happen?" But on other questions of moral and ethics it is the other way around. Nearly everyone agrees that (Y=)millions of people dying should be prevented, but not everyone agrees that (X=) it is required to cut down CO2 emission to do so. On other hand everyone agrees that an embryos dies if you have an abortion, but people disagree on the Y question: Is it a bad thing if a embryo dies?