Ill tell you how

As of now we (the human species ) have very general medicine - with alot of side effects, and then we have diseases that that medicine targets poorly. With the knowledge of evolution, and further more, with the knowledge of how our building blocks (DNA) behave we can with more precision fix ailments.

Now some people have natural antibiotics for certain diseases while others dont. Researching the DNA of these different groups can help find out what it is that makes those people immune and fix the problem for other people with greater accuracy then has ever been done before by looking at the diffirence between those two groups.

The world is a complex place and everyone can catch a disease that their body cant handle, therefore all people potentially gain from this research.

The question you started with "Is there any reason to believe evolution?" - is obviously answered by "yes" - for the evidence is way stronger then "beyond reasonable doubt"

The question You ask then "how does it benefit the average person to have a personal knowledge of the topic?" I think you are sort of backing of into a corner but I will put forward an answer for that as well; You could as well say "how does it benefit the average person to have personal knowledge of math or economics. Now if you work a normal everyday job, you might not have much use for these subjects, but that hardly support the view that then there is no reason to believe that these subjects enlighten our understanding of reality. But in general, by keeping as a big percentage of a society as we can aware of the basic functionality,s of general sciences, we make the boiling pot of generating new and better Ideas, that much bigger, and can therefore in the future enjoy even further benefits from technological advancement.

The reason scientifically minded people do not like when Creationists and their frontgroups try to put evolution down, is because the creationists do not put up a scientific argument, they put up a political argument only with the subterfuge that they need their called for political changes because "they case hasn't been settled" - but as long as Creationists cant give scientific (that means testable) evidence of the existence of a higher order that designs molecules, then It is quite devious to put all the effort to win political battles.

When DNA was discovered in the mid nineteenth century, scientist got evidence of the fact that cells are built up by computational messages (A,C,G,T acids). It is not strange to me that with our cultural baggage, alot of people would jump to the conclusion that because there is computation going on inside our cells; "then there must be a "programmer" somewhere.

In the nineteenth century scientist also started to discover alot about computation and how very simple programs can by repetition (birth -death cycle) create much more complex patterns than itself without any outside help (look at Stepehn Wolframs "A New kind of science" if you are interested in complexity theory/chaos theory) So there is alot of evidence that you dont need a complex thing (god for example) to build other complex things, you can just as well have a very simple thing that creates very complex things, that humans with all their mathematical tricks cant even forsee without just letting the simple program run its course.

Now again to your question "how does it benefit the average person to have a personal knowledge of the topic?"

If honest scientists because of social pressure, have to spend a bunch of their time correcting the same mistakes over and over again, because creationists who because of a cancerous meme called religion cant accept that their theory´s dont hold water and cant show any real world benefits, then that is a real problem for society. The chain is only as strong as the weakest link - and concerning trying to keep society afloat and functioning, it is safe to say that religious groups that want to go backwards and freeze time in the fifties so that their sense of self (that they are in the same clan as the "big boss) cant be challenged,; it is then safe to say that these people are the weakest link - and they have become hooked on ideas that have no consequence, and only get in the way of decent human endeavor.

P.s Talking to creationists I feel like I am talking to people who are sure that the world is flat, and when I invite them to go on a journey (of learning) to see if it actually is so, they try to stall to gather their clan to beat me by numbers and not facts.

My initial thought is religion. There are numerous religions that believe humans were created. With this knowledge, people might revoke religion entirely, which may be the single greatest thing to ever happen.

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Beides, just because I will never use fractal mathematics in my everyday life does not mean there is no use in knowing it. Having knowledge is the only way we can come to understand the world we live in. Hell, one could argue that we don't need any extra knowledge at all and that we would be fine just eating sleeping and dying. But what kind of a life is that?