If you are tired of people accusing you of being "biased" or "closed-minded", then you must make an impression to others that you have an open mind. Such techniques include accepting their opinions seriously. Take what you agree from them, and reject the rest. And if their opinion is not supported by evidence, assume that they might be right in some aspects, assume if some premises are true and then consider if their argument still holds, and research their opinions by yourself. If you do not let them know that you are listening to others, then others will see you as "closed-minded" and thus "biased."
Never reject their opinions even if they do not cite their sources of what they come from. Do not blame them for not referencing studies or links. Do not blame them by saying that you should be responsible for the "burden of proof." It is up to you to provide the "burden of proof" at all times, even if "he's the one who is responsible."
That may seem unfair to you, like a double standard: They should be allowed to express their opinions, without citing their sources; then why shouldn't you be entitled to that same luxury? But think of this: if you do the same as they do, then other people will accused of being "biased" or "closed-minded." So if you do not want people to call you "biased", then you must accept that double standard. People are quick to judge one another as "closed-minded" even if both are playing on the same level.Also, if they gave advice without supporting evidence, it is just what they have to share in mind. This does not necessarily mean that they do not have evidence. They could mean that they do have evidence and studies which support their position, but they were just too lazy to provide references for the studies or articles which support their opinion. They do not want to write a long comment which no one is going to read.
If you disagree with someone, do not just say it. Cite your sources and provide proof that you disagree. All statements should be cited fully, no matter how minuscule it is. If you are too lazy to cite your sources, then do not mention your disagreement at all. Saying stuff without citing sources will make you lose your credibility.
Even if they don't cite any sources for their arguments, you should still cite your own arguments. This seems like a double standard, but if you don't want people calling you to be "biased" or "closed-minded", then you have to do this.
Even if they are "wrong", support their main point. Even if they are "wrong", you should still interpret their theories in a way so their theories can be true, in some aspects or conditions.
Likewise, do not accuse others who provide no references as ignorant or biased. As said above, people may just be too lazy to bring up links to support their position.
People with strong contrary opinions will rationalize away your evidence, unless you do an exhaustive and complete dissertation of your position, including counterarguments to all possible "holes" in your opinion.
In addition, avoid all vague statements, such as "everyone is different", "everyone is the same", "diets should be relaxed", "there should be limits on diets", "certain foods should be restricted". The last statement has problems with vagueness, because it does not specify what exact foods which should be restricted? Processed foods? Restricted at what levels? How much you should restrict them? Does that restriction allow "cheat" days? But people generally interpret such statement with such absolute sense, even if they are just exaggerations. This is the problem with vague statements. People talk over one another, and the statements, which are exaggerations, are interpreted literally when they are just trying to make a point.