Lets say that for some reason, Spottedleaf never receives the prophecy: "Fire Alone Will Save Our Clan", and Rusty never joins ThunderClan.

It might have a greater impact than you'd think.
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1: After Redtail's death, Lionheart is still made deputy.

2: Ravenpaw would have had a different fate. Though it's possible that he might have told Graypaw that Tigerclaw murdered Redtail, let's say he was too afraid to. Tigerclaw ends up killing Ravenpaw, but tells the Clan that it was an accident. They believe him.

3: Yellowfang is never taken into ThunderClan. She would likely have been driven out of their territory, and stay a rogue.

4: ShadowClan would likely still have attacked ThunderClan, resulting in Lionheart and Spottedleaf's deaths. Tigerclaw is made deputy, and the Clan is without a medicine cat. Bluestar and Tigerclaw know that they are in need of a medicine cat. Tigerclaw might have suggested making Darkstripe or Longtail medicine cat, or Bluestar might have sought out Yellowfang aftet hearing she'd been exiled from ShadowClan. Another possibility is that StarClan sends a sign regarding which kit to make the next medicine cat (That could have been Brackenfur OR Cinderpelt), and that cat would be trained in dreams similar to Willowshine's case.

5: Brokenstar does not lose leadership in ShadowClan. However, some cats such as Flintfang begin planning to overthrow Brokenstar.

6: Eventually, Tigerclaw succeeds in killing Bluestar, of course hiding the fact that he killed her from the Clan. Tigerstar becomes leader, and makes Darkstripe his deputy.

7: WindClan would probably have returned to the forest at some point.

8: Brambleclaw and Tawnypelt both grew up in ThunderClan. Not knowing of their father's crimes, they would have admired him.

9: Tigerstar and Brokenstar merge their Clans. Some of the ThunderClan cats begin questioning Tigerstar's leadership, and talk about this privately with the cats who question Brokenstar. They plan to rebel.

10: Brokenstar and Tigerstar would probably grow tired of having a shared leadership, and eventually, one of them kills the other. Quite possible for both of them. If it was Tigerstar who died, cats like Darkstripe would have grown angry and challenged Brokenstar's cats. If Brokenstar died, cats like Blackfoot would be angry and challenge Tigerstar.

11: RiverClan and WindClan form an alliance to stop ShadowClan and ThunderClan. The rebelling ThunderClan and ShadowClan warriors secretly help them plan an attack. There's a battle, and who knows who wins.

Long term effects:
Squirrelflight and Leafpool are never born, therefore the Power of Three are never born, therefore without preparing for the attack, the Dark Forest wins the final battle.