From the combination all the plot lines.
It seems to me that Kagha wants to close off the grove so that the shadow druids can have an easier time taking over the grove AND keep safe from goblins. They don't want the tieflings maybe partly due to what happened before with the town descending into hell (these are the tieflings that were part of that.) The druids were conflicted in keeping the tie flings because they just became leaderless and Kagha was a strong figure to band around to (This type of stuff happens) They are leaderless because the goblins captured Halsin. Halsin said that the goblins were causing an imbalance. So as a druid, killing/stopping the goblins is actually GOOD.
The tieflings were bringing in goblins attacks. Thus the tieflings were also causing an imbalance. So Kagha, a member of the shadow druids, decides to close off the grove. If she really was 100% committed to shadow druid ideology, she would've just killed the tieflings herself, but she was trying to radicalize the grove into shadow druids.
Refugees from Hell have come to reside in our grove after a pretty large incident concerning Hell.
Leader taken by Goblins
Goblins are attacking trying to kill refugees.
Shadow Druids try to fill vaccum- Blame refugees for goblin attack
PC can either help tieflings or let them die.
Kagha don't care as long as they are gone before they close off the grove so she can take control
Shadow Druids are pretty harsh when it comes to anyone messing with nature. Now imagine a Hellspawn (Which already get bad rep) taking one of your relics. They gonna be pissed.
I don't really understand the disconnect here.
If a certain race of people with a bad rep come to a grove that is being taken over by extremists that believe anything that upsets with nature and balance should be destroyed or leave then I don't find this arc to be too unbelievable personally.
A few notes:
-There is a shortage of resources at the grove. The halfling trader mentions this for example, the druids cannot feed the tieflings.
-Tieflings are not "denziens from hell" they are people who have devil blood in their ancestry. A cambion (Mizora and Raphael are cambions and the creatures fighting the Illithids in Avernus are cambions) is someone born directly from the union of a material plane denzien and a devil).
-Shadow Druids simply don't want people of any kind around. They are isolationists who believe nature can only be protected if the world is brought back to a primordial state by any means necessary, which usually means killing people. They don't want the tieflings in the grove not because they are tieflings but simply because they are not shadow druids.
-Kagha is not a Shadow Druid (yet) when you meet her. She's falling for them though. You have the chance to prevent this from happening.
-If you listen to Kagha and read her correspondance with Olodan you learn that Olodan KNEW about the assault on the grove and offered Kagha a way out IF she was willing to bring the grove under the Shadow Druids control. It's very possible the Shadow Druids are part of the conspiracy threatening the Sword Coast.
-Also, Silvanus' Grove is important to the plot. The druids were the ones helping the Selunites stop the forces of Shar years before (check the murals inside the grove). The tadpole is protected by netherese Shadow Magic which was the gift of Shar to the Netherese survivors of Karsus' Folly (the Shadovars). All of this is connected.