In the original R18+ PC game, the route order was restricted, so the play order is enforced:
- Unlimited Blade Works (complete Fate)
- Heavens Feel (complete Unlimited Blade Works Good or True Ending)
There was also a way to enter the Unlimited Blade Works route without completing Fate from Day 4. However, it locks you into a Bad End for Unlimited Blade Works Day 5 and Bad Ends don't unlock routes.
Source: Full Image of the Mirror-Moon.pdf
Because Realta Nua PC is 3 separate games, each being each route, there is really no restriction. However, from my understanding, the plot is not changed, so some reveals such as characters and abilities are glossed over when they appear again in a new route e.g. Rider's identity is revealed in Fate but from my recollection is glossed over in Heaven's Feel because of the original assumption that the player had already completed Fate. Not to mention the impact of certain events in Heaven's Feel does not hold the same weight if it was played first.
While there is nothing stopping you from playing any order you want, my personal suggestion would be to follow the original game's enforced play order: Fate > Unlimited Blade Works > Heaven's Feel.