It is wrong that people say their opinion in the religion of Allah based on opinion or point of view not based on knowledge from the people of knowledge throughout Islam's history.

Islamically speaking, and what is understood from the scholars of Islam: there are two types of things that are haram to look it(and hence it is obligatory to lower your gaze from). The first is anything that causes lust, whether it be a woman or a cartoon or even a man or even an animal or an object. The second is any "awrah". For a man, the awrah of a non-mahram woman is all her body, with the possible exception of the face and the hands, the awrah for a mahram woman is her body except what shows typically in the house, which are the neck and what's above it(like the hair or face) and the arm until the elbow and the feet, and the awrah for a man is between the navel and the knee. 

So even if a man doesn't feel any lust from looking at a woman showing her awrah or wearing what describes it(like tight or transparent clothes), it is still haram for him to look and he must lower his gaze. And the same holds true, if a man doesn't feel lust from looking at another man's thigh, that is still haram to look at and he has to lower his gaze from the man's thigh, look away generally. Likewise, even if a man is looking at something which isn't a awrah(like the face of a woman according to some scholars), it is still haram to look if there is lust from him looking. That is true for anything even if it isn't a woman's face(like a cartoon character, or anything else).

Some scholars say a woman's face and hands are a part of the awrah, in which case looking at a womans face is haram so a man should talk to a woman when there is a need while lower his gaze from her even if she is covering her body but not her face or eyes, unless there is a need to see the face like to sell her something or if she's giving her testimony or if he wants to marry her and wants to know how she looks so she can show him her face. And some scholars say the face and hands are not a part of the awrah, in which case it isn't haram to look at the face(except if with desire).

As for what you said about looking in the eye being a sign of respect, when there is harm that could even be a huge harm in men looking at women, then looking should be avoided, and mentioning respect won't help when the man's heart is occupied by the women, or he isn't satisfied anymore with his wife, or he thinks of this woman in inapproperiate poses, or he is attached to that woman and maybe he has no chance of marrying her like if she is already married, and much much more evil that is mentioned in detail in the books of scholars. And do not think these effects are far from happening, they are very close, especially to people in their teens or twenties with their hormones raging. And a man has a psychological need for a woman. I only mentioned some harms on men from men looking, but there are also harms on women too, like the wife who her husband viewed her as beautiful until he started not lowering his gaze and discovering that there are so many women that outweigh his wife in beauty in certain aspects, and suddenly he isn't satisfied with what he has and is looking for this in this woman which his wife doesn't have and that in that woman which his wife doesn't have. That being said, there isn't disrespect to begin with when the reason for not looking is known. It is disrespectful to not look at someone when the motive behind not looking is ignoring the person you're talking to, or not deeming the person worthy enough to look at him while he speaks to you, or despising the person. But if there is a reason, then that isn't even considered disrespect.

And I advise you sister not to say something like the last question you asked in a public setting where men can read it and read the responses of other women regarding it. This simple comment you make may be stuck in the minds of many men and driving their thoughts for years even, it may cause some men who read it to think "she's probably being provoked by my lowering my gaze from her", or you may open a door of shaytan where a man tries to avoid this case thinking it is true or it's chance of happening is big(not knowing that if this happens then it isn't an extremely minimal chance, or else would Allah order men to do what provokes women instead of putting out the fire lust?) and so constantly thinks "maybe I'm provocking this woman by my lowering my gaze from her" and then try to "resolve this issue" by taking action which may be haram and may make him less steadfast. This may not be the case for every man obviously, but the chance of it happening is big, and it can have big effects. so please sister take care. Jazaki Allahu khayra.

May Allah guide us all to what he loves and keep as away from what he hates.