It’s a good question, that I fear may not have much of a satisfying answer.
For orcs, 33-40 years have past since they were slaughtering Draenei on Draenor. Those that took part are in it will have grey hairs now, those that yet live. And how they feel about it, and how they raised their kids to feel about it, will differ from Orc to Orc. Thrall seems to acknowledge they have legit beef with the Orcs. Saurfang and many old Orcs likely look back on those days with regret at being used by demons, and committing atrocities that are hard to justify. But certainly there are Orcs that will remember the glory of victory, and glorify the period, as well.
I do not RP Alliance, but I would imagine most Draenei played are very much of the mindset that this is just recent history. Now, Draenei are overall not a hateful sort. And I’m sure a good number, like Velen, will mostly hold the Legion responsible. But personal hatred is a powerful thing. And Legion or not, the ones doing the genocide had orcish faces. So while most Draenei may prefer to keep the peace, I’m sure resentment must exist in many.
That said, there doesn’t appear to exist more hostility between Orcs and Draenei than generic Horde and Alliance races. The main beef seems to be the more recent Orcs vs Humans. I’ve seen more hostility from Night Elf roleplayers (pre Teldrassil) against Orcs, than Draenei. And Draenei have never treated the Orcs with specific hostility that I remember. What we’ve seen more of, is Orcs interacting with Draenei. The Orcs that came with us to WoD’s Draenor, Thrall, Eitrigg and his son, had no issues coming to the aid of the Draenei. Maraad was the Azeroth Draenei of note coming along, and they fought Iron Horde Orcs shoulder to shoulder.
That’s not 100% conclusive, of course. But I think we can at least infer that the majority of Orcs and Draenei, are at least able to set aside past grievances for the greater good, when the time is right. Be it through Orc guilt, or Draenei being able to judge people, rather than races.
In RP, I’ve found the interaction to be cautious, sometimes even awkward, but rarely hostile. That said, it is likely there’s a significant number of them that do hold resentment or hostility, and would be eager for a fight when things turn hostile. There’s enough factors and variety here for a character to be in line with the lore, with either perspective.
As for me, my Orc grew up on tales of her parents. Stories of the dark deeds they committed in the past, to warn her against such a path. She would prefer never having to spill blue blood.