Dove and Tiger are not acting OOC
I'm mostly repeating myself from a comment I made on someone's post about this, but I have seen soooo many people being angry about how Dovewing and Tigerstar act when Birchfeather expresses his desire to leave ShadowClan for Ridgeglow in SkyClan.
Rowankit died and we see on page how devastated they both are, I imagine they kept Birchfeather very close and probably hovered over him as the only surviving kit of that litter. They support cross-clan relationships but they clearly never expected that their youngest kit would want to leave them and their Clan. It shook them. It probably felt like losing Rowankit all over again. They were also protective over Shadowsight in TBC, I imagine that was dialed up much more for Birchfeather. Yes, they aren't being fair to him, and a lot of people don't like how they're handling him leaving ShadowClan, but I do not see how they're acting as being out of character.