Sounds like some quest isn't remembering to set its relevant markets as non-story-critical when it completes (or perhaps when that quest is skipped in Nex; also found that Kanta's Den is always protected).
Copy-paste this into Console Commands console to find and remove:
runcode import com.fs.starfarer.api.campaign.rules.*;
for (MarketAPI market : Global.getSector().getEconomy().getMarketsCopy()) {
if (Misc.isStoryCritical(market)) {
MemoryAPI mem = market.getMemoryWithoutUpdate();
Console.showMessage(String.format("%s is story-critical, displaying reasons and unprotecting", market.getName()));
for (String reason : mem.getRequired(MemFlags.STORY_CRITICAL)) {
Console.showMessage(" - " + reason);
}
mem.set(MemFlags.STORY_CRITICAL, false);
}
}
In case you were wondering, here's what I got after using all the quest skip options:
Imperial Embassy: ii_no_invade (modded, so not super relevent)
Kanta's Den: gaATG (should be at the gates) and pkl (no idea, maybe pirate crisis?)
Tartessus: bffi (false idols quest)
Hesperus: lpp (pilgrim's path?) and bffi
Gilead: lpp, lke (knight errant?) and bffi
Asher: bffi
Kazeron: gaATG, bffi
Chalcedon: lke, bffi
Olinadu: bffi
So it looks like there might be some problem in False Idols, Pilgrim's Path, Knight Errant, At the Gates, and whatever pkl is. I don't know if the problems persist if you complete the quests normally, I only used the new story skip configuration at the start.