Without seeing more it's hard to say what the author meant. Also I'm not sure if he means:
- respect to a non-Muslim (as a person)
- respect to a non-Muslim's action
If he means action, well if it's a good action then it deserves praise regardless of who's doing it, Muslim or not.
If it's about a non-Muslim person:
About people of the book:
Indeed, those who believed and those who were Jews or Christians or Sabeans [before Prophet Muhammad] - those [among them] who believed in Allah and the Last Day and did righteousness - will have their reward with their Lord, and no fear will there be concerning them, nor will they grieve. Baqara : 62
About respect to others (atheists or non-Abrahamic follower, not that they are the same, but...)
Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.Mumtahana 8
So we are encouraged to be righteous towards and acting kind towards anyone who doesn't fight against us in religion & expels us from our homes.
For those who expel us from our lands, it's obvious. The tricky part is for those who fight us in religion, like people who mock us praying, mock us having hijab, mock us who believe in God...for those people we are encouraged to socialize differently. Not that we should show them injustice or oppress them, but the level of kindness should certainly be different from some other atheist who just minds his own business and greets us, socializes with us and doesn't mock us.
In addition we have also been discouraged to take any non-Muslim as a guider.
They wish you would disbelieve as they disbelieved so you would be alike. So do not take from among them
allies masters (one who you listen to as having more authority) until they emigrate for the cause of Allah . But if they turn away, then seize them and kill them wherever you find them and take not from among them any ally or helper.Nisa' 89
As for the violence of the verse. Please my answer here. Basically it applied to very specific people who were peace breaking killers
so basically we are to dislike, those who expel us from our land, mock fight us in religion and not to take them as our guiders/masters.