There is no doubt that there are many differences of opinion amongst Muslims in matters of the prayer, as well as many other matters. This is something that the Prophet (may the peace and blessings of Allah be upon him) foretold, when he said:
"Indeed, he among you who lives long will see great controversy, so keep to my Sunnah and to the Sunnah of the the rightly guided caliphs, those who guide to the right way. Cling to it with your molar teeth. Beware of newly invented matters [in the religion], for verily every innovation is misguidance." [Abū Dāwood: 4607]
This narration provides us with everything that we need to deal with this situation of differing, and from it, we can extract the following methodology:
Whilst it is sometimes the case that there is more than one way to do something, and that more than one opinion is right (such as different supplications that can be said throughout the prayer), the majority of cases have one right opinion and others which are wrong. This is clearly illustrated in those narrations which forbid something, and the Muslims disagree about what is forbidden. For example:
"When any one of you prostrates, let him not go down as the camel does"
The scholars differed over what this means, forming two groups. One group said that it means don't put your knees before your hands. Another said that it means the opposite. What is immediately clear is that both of them can't be true. Therefore, we are commanded to strive to come as close to the truth as we can.
As for crticism of other people's opinions, it depends on the basis of their opinion. If their opinion is based upon a weak or fabricated narration, then it is deserving of stronger and more vocal criticism than if their opinion has a strong body of evidence, but you believe the balance of evidence to show the correct answer to be something else.
On this website, we have strived to present the strongest opinion for each issue, and we have limited the mention of disagreements. This is to make the site easy and accessible for people of all ages and abilities, as well as new Muslims.