In my experience, respect is best described as when a person engages with you while demonstrating that they value you as a person...even if they are voicing disagreement.
In a world seemingly dominated by loud voices and big egos spouting opinions and irrational nonsense with unearned confidence, it is increasingly common that respectful, compassionate, and rational communications are met in a disrespectful manner. This is especially prevalent on the internet, where a culture of disrespect has been allowed to flourish. Here, toxic personalities try to exert power over others while hiding behind the relative safety of distance and anonymity. They may try to diminish your point of view, silence you, obscure the truth, or bait you into various conversational traps.
It can be immensely frustrating and it may not be obvious at first as to how much power you actually have in these kinds of situations. You do not need to engage with toxic personalities or audiences at all. The greatest power that you can wield in the face of disrespect is Silence and Distance.
It is important to remember that respect is something that is given and received. When someone (especially people you don't know) shows you disrespect, they are showing that they are incapable of treating you with decency. Nothing you can do or say will ever teach someone to respect you if they demonstrate no capacity for respect in the first place. Engaging with disrespectful people just invites more disrespect.
This is especially true with those dangerous personalities that psychologists refer to as "The Dark Triad": psychopaths, narcissists, and machiavellians. These personality types can never demonstrate true respect for other people because they are incapable of empathy and compassion for others. And unfortunately, they are surprisingly common, with estimates that up to 7% of the population exhibits these traits. However difficult it may be to detect the manipulations and dishonesty of these people, they cannot help but "leak" disrespect because at their core, they just see you as a tool to be used or abused. The best strategy for avoiding these types of dangerous personalities is to disallow disrespectful behaviour in your life. The power of silence and distance will save you from immense grief in the long run. Politely disengage and never look back.
In both positions of leadership and in my personal life, I have seen all kinds of identical situations handled by some people with polite respect and others with terrible disrespect. Those that have the audacity to engage in disrespectful behaviours get the silent "cut from team". Those that engage with respect get my respect, even if I disagree with them.
You are the gatekeeper to your own life. If a person or audience is not showing you respect, they do not deserve further engagement from you whatsoever. For your own health and well-being, cut them out immediately and carry on.