Do Buddhists think other religions are wrong?

Talking about Buddhism as a whole it's rather difficult since there are many views and ideas. Many people would tell you that's harmful, others would tell you that it's ok. What I'd tell you and I think it's the most accurate is that in the core teachings, it's as irrelevant as it is relevant, which means "it depends".

Religion is often used as an excuse to not think, not see the life according to your own view, and in general drift from reality to something that intellectually is more appealing to ourselves. Some other times it's used as 'imposed beliefs', which we follow naively without question; each being has it's own realization path and it's own state of mind, preferences, personality and so so, thus, it could make him/her confused and drifted as to what he actually believes and thinks. When such is the case, indeed, religion is poisoning us (even if it's "buddhism") and making us go into samsara or conditional suffering.

Beliefs are not against buddhism in any way, as long as it's of good use to you and others.

“It is impossible, mendicants, it cannot happen for a person accomplished in view to dedicate themselves to another teacher. But it is possible for an ordinary person to dedicate themselves to another teacher.”
AN 1.276

"A person accomplished in view" refers to a stream enterer.

In the sky there is no track, there’s no true ascetic outside here. People enjoy proliferation, the Realized Ones are free of proliferation.
Dhp 254

"True ascetic" refers to stream enterers, once-returners, never-returners and arahants. "Here" refers to the Buddhist path.

An alternative approach is to consider what Lord Buddha taught to whom. For instance, he did not teach vinaya to laypeople. What we can learn from this is that he adjusted his teaching according to his audience.

How can he do this? Because Buddhism is not dogmatic. Buddha taught contextually, in accordance with the needs, convictions, and views of his audience. He was also sensitive to their beliefs.

Did he speak out against certain religious practices? Yes, definitely, but with great hesitation. For instance, the 'dog-duty' practice, or the 'ox-duty' practice (MN57 - Kukkuravatika Sutta).

If Buddha were to give a talk to christians, in a region where non-christians would come to harm, would he talk against their beliefs? I doubt it.

If Buddha were to give a talk to muslims, in a region where non-muslims would come to harm, would he talk against their beliefs? I doubt it also.

The term religion is just a synonym for a world-view and there are many wrong ones but only one right view, regardless of how any of them are labelled. The one right view concerning suffering, its cause, its annihilation and the method for its annihilation is actually the timeless essence of all existence, while how much of it is understood and practiced does indeed vary in time and space.

Delving into a comprehensive study of comparative religion per se, in order to see how much Truth can be found in each particular world-view, each with its inherent jargon, would be a different topic altogether. But there is nonetheless only one true and correct answer to the problem of salvation from suffering, in Pali terms - Dukkhanirodhagāminī Paṭipadā Ariyasacca

The Theravadan Buddhist perspective says that Buddhist has a pluralistic view of religion. The Buddha was suggested to say the following about the validity of other religions in the Mahaparinibbana Sutta.

"In whatever Dhamma and Discipline the Noble Eightfold Path is not found, no ascetic is found of the first, the second, the third, or the fourth grade. But such ascetics can be found, of the first, second, third or fourth grade in a Dhamma and Discipline where the Noble Eightfold Path is found. Now, Subhadda, in this Dhamma and Discipline the Noble Eightfold Path is found, and in it are to be found ascetics of the first, second, third or fourth grade."

The "Noble Eightfold Path" is a group of 8 "corrects" that when put into practice lead to Enlightenment. These 8 are correct view, correct intention, correct speech, correct livelihood, correct effort, correct mindfullness, correct meditation.

Note that these 8 "corrects" are qualities that can be done and are done in other religious (and non religious) groups.

While all Buddhist accept these 8 "corrects" as needed to reach Enlightenment, they have a lot of disagreement of how to define them.

Some Buddhists sects view "correct livelihood" to mean vegetarianism is necessary, while other sects view it is not necessary.

Some Buddhist sects view chastity as necessary to achieve "correct meditation", other sects do not view chastity as necessary or beneficial towards "correct meditation".

Within the religion, many Buddhist accept the view that there are many roads leading to the same place.

While other religions may not call living virtuously and with self-restraint, the "Eight Noblefold Path" and may call it "The Ten Commandements" or "The Word According to the Book" are they not really the same thing?

Perhaps there are some sects of Buddhism that preach salvation, but there is no god to save us in Buddhism, and there is no one that can be saved, and there is nothing that we need to be saved from. So salvation in Buddhism has no place to take root. The Buddha replied to an inquiry about who he was. He thought for a while and said "Awake." That same awakeness is here right now whether we are aware of it or not. If you want to read about Zen, you will find no salvation or hope of it. www.arvindguptatoys.com/arvindgupta/zenmind.pdf

But to answer your question, I would find any sect that denies any other religion difficult or impossible to defend as Buddhist. They violate one of the most sacred principles, Do No Harm. Denying any other religion is an attempt to harm another's path to awakening. If someone worships a rock, even that is their path to awakening. When the pursuit of awakening supersedes the pursuit of having the most powerful religion, we will have no reason for such debates.

The following seems to be an apposite quote for this question.

The commentary to the Shorter Discourse on the Lion's Roar says that the following quote says that eternalism and annihilationism are, both, views which do not lead to liberation i.e. the end of suffering.

6. "Bhikkhus, there are these two views: the view of being and the view of non-being. Any recluses or brahmans who rely on the view of being, adopt the view of being, accept the view of being, are opposed to the view of non-being. Any recluses or brahmans who rely on the view of non-being, adopt the view of non-being, accept the view of non-being, are opposed to the view of being.[5]

7. "Any recluses or brahmans who do not understand as they actually are the origin, the disappearance, the gratification, the danger and the escape[6] in the case of these two views are affected by lust, affected by hate, affected by delusion, affected by craving, affected by clinging, without vision, given to favoring and opposing, and they delight in and enjoy proliferation. They are not freed from birth, aging and death, from sorrow, lamentation, pain, grief and despair; they are not freed from suffering, I say.

The commentary says,

The view of being is identical with eternalism (sassatavada), the positing of some eternal entity or spiritual principle, i.e., a substantial self or soul, as the essence of the individual, and the positing of an eternal entity, such as a creator God or metaphysical Absolute, as the ground or source of the objective universe. The view of non-being is identical with annihilationism (ucchedavada), the repudiation of any principle of continuity beyond death and the denial of an objective, transpersonal foundation for morality.

There's more (which I haven't quoted) in that commentary.

The existence of 'Right view' implies that there also exists such a thing as 'wrong view'.

In Buddhism you have to straighten your views. In this process there may be times where you new views might start contradicting your previous beliefs or that of established religions. There are 3 stages to straightening your view:

1. You learn the Dhamma and see that this sounds right
2. You see it is logical
3. You practice and empirically verify and see that it is in fact true.

As a person taking the path you need not put aside any views as right or wrong to start with just because it is said so. Through logic and practice you start seeing things clearly then you can straighten your views. When you experience some thing sometimes even a a firm believer in Buddhism you would start seeing things in a new light and sometimes see your initial conceptual understanding differs from reality.

Hence the Buddhist position would be that conceptual / philosophical understanding is flawed. Your understanding is right only with regard to what you see at the experiential level. Hence any philosophical / conceptual aspect of any religion including Buddhism cannot be absolutely right.