The 27-year-old winger turned his back on the Millers at the end of the season, rejecting a new contract in the hope of staying in the Championship.
However, that did not come to fruition and he instead ended up joining Saturday's opponents Doncaster Rovers after the season had started.
That has earned him some criticism from fans on social media, but Warne is desperate for that not to carry over to the game at the Keepmoat Stadium.
Over 3,000 Millers fans will make the journey up the M18 and the boss is pleading for some respect to their former player.
"I want us to be better people really," he said. "Please don't go to the game and think, 'Great, I'm going to have a few beers and then abuse one of our old players'.
"He was a great servant for us. He gave everything he could for us on a daily basis. On a performance basis, he was great.
"All the players who have played for me at this club will be loved by this club, I'd like to think. I don't want our fans to think, 'Ooh great, we can give Tayls some.' I think it's disgusting.
"I know some fans will read this and think I'm wrong. It's my opinion and I'm entitled to it, as you are yours."
Taylor was the club's record buy when he arrived from Peterborough in 2016, but despite making over 100 appearances for the club there was always a sense that he did not quite deliver.
There was no questioning his work ethic and Taylor wanted another crack at the Championship following the club's relegation.
Warne added: “I offered him a contract but he chose to leave for two reasons really.
"I couldn't guarantee him that he would play every week. I can't give that guarantee to any player. I will not do that.
"Also, he truly believes through his own confidence and through his agent possibly that he could still play in the Championship. And why not?
"The fact that he had got employment down the road at Donny ... so what? Bless him, he deserves to earn a living. I don't understand the anger."
Kyle Vassell will miss out for the Millers with a hamstring injury while goalkeeper Daniel Iversen is on international duty.