Yes. Absolutely yes, there should be reasons for beliefs. Why?
For one thing, if you don’t have a reason to believe something, then you have no ground to stand on if you want to argue for your position over another. This is also true if your reasoning is not sufficient, but for now I want to focus on whether you have a reason at all. For another, how else can you claim to know anything?
My most foundational belief is that conclusions and beliefs should be justified by reason and/or evidence. For instance, when I was Catholic, I believed that Mary was born without Original Sin. Why? Because the Catholic Church taught this, and the Catholic Church (I thought) is an authority because it was founded by Jesus, who is God, who would not lie and promised to protect His Church from teaching falsehoods. I also had arguments for why I believed Jesus was god, but I’m sure most of my readers are familiar.
Side note, this is one of the few things I still admire about the Catholic Church: it at least tries to claim that it is reasonable. It isn’t, of course, but at least that is the ideal it aims for, and that is my same ideal.
As a materialist, I make just a few foundational assumptions. First, I assume that an objective reality exists. Second, I assume that my senses more or less accurately report that reality, as do most other people’s, and that they will continue to do so. Finally, I assume that reality will continue to exist in more or less the same way it always has – that is, that observations made by my senses can be used to predict future observations that I will make.
I think we would be hard pressed to find anyone who does not operate under these same assumptions, whether they realize it or not. This is precisely why it offends me so much when someone claims that atheism requires faith, especially as much faith as theism: not only does it ignore that atheism is nothing more than the null hypothesis, but it also ignores that everyone operates under exactly the same principles that even can be argued as faith-based in my worldview.
Someone might claim not to accept the few foundational assumptions that I do, but I think that person would likely still act as if they accept them. In other words, they would still not walk into a street if they saw a car coming because they assume that the car is really there, they are right in seeing it as really there, and they can predict that it would continue moving in the direction it currently is based on previous observations of cars. As I said, these things are foundational. Everybody accepts them. At least, almost everybody.
For everything else that I believe, I have at least one reason. I do my best to follow the evidence where it leads and to avoid logical fallacies in my reasoning. I cannot see how anyone can act in any other way except through pure ignorance.