Each single religion thinks other religions are irrational. Freethinkers simply take an extra step and instead of regarding all religions but one irrational regards them all as non-rational and/or irrational.
A belief when stated can be obviously irrational. The only proof that somebody is irrational is when they open their mouths. The notion that rational people can believe in irrational things and still be rational is dangerous. Usually what happens is the person says something insane and people judge him rational because of his genius in many matters and his use of logic. But the fact remains that none of that proves his insane belief is rationally held. His rationality has to do with other things not this one. And you would have to be him and see his thinking processes and see how he arrived at the absurd belief before you can say he at least thinks he is rational. Nobody can do that so a belief that looks irrational or to be at least non-rational should be considered guilty of irrationality until proven innocent.
Saying somebody is convinced about their belief being true is a way of arguing that their position should be considered. That may not be the intention but it is obvious that a belief held deeply and in a very convinced way may have something to it. That is why if a belief that is too far-fetched or dangerous or held too strongly it needs to be challenged.

Somebody has an irrational belief. The evidence in logical order of importance and usefulness for the person being irrational at least with this particular belief is:

The clear irrationality of the belief and the terrible or non-existence evidence for it. Remember that evidence for the irrational is an abuse of evidence and is not evidence at all.

The evidence that the person is holding the belief rationally though it is still wrong is more of an indication than evidence and thus is not very strong. It cannot be strong.

And you cannot know if there is evidence or if the evidence is understood properly for you cannot become that person to think like they do.

And the proof that they are rational in so many things is irrelevant.
So the buck stops here: an irrational belief needs to be taken as a reflection on the irrationality of the holder.

If religious belief is irrational then it follows that the people were not reasoned into belief. Some say that you cannot be reasoned out of beliefs you were not reasoned into. Only luck then can help you. Others say you can be reasoned out but it can be a long difficult process. The latter considering how much each generation changes its mind about stuff that seemed set in stone forever before is probably the correct view. People accept this view for if they didn't nobody would bother trying to talk sense to anybody. People need help in reasoning before they can be reasoned out of anything. They need to be shown how to think coherently. But we can be sure that there are many no matter how much help they get will still accept religious nonsense. And a child or very young person will be hard to reason out of religious belief for they believe for they are conditioned and programmed to.
Not all religions claim to be rational. Incredibly Christianity despite its outrageous doctrines claims to be rational. Having reasons to believe something does not prove that the belief is rational only that the belief is trying to be. An irrational religion believes in things, things may be true or false, for stupid reasons. A correct and good belief can be irrational if it is accepted for the wrong reasons. No religion should claim to be rational - no rational religion would! It should demonstrate its rationality.
Many faiths are just polar opposites. There is the belief that there is no spirit but only matter. There is the belief that a man and woman should marry and be monogamous and there is the belief that a man can take as many wives as he wishes. There is the belief that capital punishment is fundamentally wrong and the belief that it should be allowed for lots of "crimes" including losing your faith. There is the belief that messages from God should be full of peace and love and wishy washy and there is the belief that God wrote the Bible despite the fact that it contains abusive and nasty messages and advocates murder in his name. The people that hold these beliefs cannot be equally rational. People judged as educated and intelligent defend them. It could be that a person believing in any messages alleged from God is irrational but surely the one who believes the pro-violence ones is more irrational than the person who believes in sweetness and light messages? Religion has got power and credibility through having educated and intelligent members. People believe because of this. But in fact it is totally irrelevant. And besides you cannot believe in religion and the huge claims it makes because intelligent people seem to believe or proclaim their faith. If you believe say in God and what he has supposedly said because smarter people than you seem to, then you are idolising those smart people. You are believing because of them. That is glorifying a human interpretation. God and how he is interpreted are not necessarily the same thing. Interpretation is risky. It is always about wanting to believe what somebody else says and thus making a God out of their religious speculations. It is idolatry.
Christianity does not like to be called irrational. But it is. It makes assumptions and makes serious claims but cheats people by not giving them or by being unable to give them good enough evidence to back up the claims. It is strange that Satan and the Demons as the letter of James tells us, have the evidence that God exists. We do not. The demons have witnessed the miracles done by God while we have to depend on what people who fancy themselves as historians say. If God finds it okay to let evil beings have the evidence then why not us? He is inferring that there is something evil about having suitable evidence. Christianity, and Roman Catholicism is very vocal in this issue as is Bible based Christianity, teaches that to fail to believe in what it teaches is a sin that will lead to damnation in Hell forever. Catholics call it a mortal sin and say it is so serious for you cannot connect to God who is goodness itself without understanding and accepting enough of what he has said or revealed. The only possible way one could take such a position on unbelief is that: "If people who don't believe thought about it enough they would believe." For that to happen, it has to be reasonably straightforward to show the faith is a plausible and good thing, the best faith to have. But it is not. The evidence for any specific set of revelations be it Mormon or Catholic or whatever is simply insulting. The real purpose of the doctrine that unbelief is a sin is to scare people into belief and to insulate them against the insights of unbelievers and other religions. Ecumenism is just a window dressing. So we see that because there are so many differing faiths that disagree on what doctrines matter most and what don't and on what God has revealed, if there is a true religion, the evidence for its having a genuine divine revelation will be impeccable or at least of a standard that outranks all the the rest. It would mean however that most religions if not all are irrational.
I borrowed the following paragraph from an ex-Christadelphian website.
Humans are not “rational” thinkers; they are “rationalising” thinkers. They spend 99% of their time seeking to find evidence to support what they already believe about their choice of partners, choice of school, car, home, political allegiance, household appliance, favourite brands etc AND their choice of religion. We “rationalise” the evidence to support what we have already decided. We also “rationalise” evidence to suit conclusions that we have decided on the basis of emotional decision-making, which is how most of our decisions are made. That’s why we make so many “human” mistakes; because we are not clever enough to adequately assess all of the available evidence, so we take short cuts and use our emotions to make the decisions on the basis of passion instead. We are not slaves of reason, we are slaves of passion.