I investigated this some and it appears that at least in my case this happens for trees in new chunks generated while this mod is installed (they show up in blue on the map instead of green). The fact the issue only happens for newly generated trees might be why it appears to work if you install it later in a run, I'd be curious to know if new chunks show problem tree. I am playing with Alien Biomes and Krastorio which might part of the problem, I don't know.
The issue appears to be that Blueprint Trees generates duplicates of trees in the game. They are named like "BlueprintTrees-X" where X is the original name of the tree in the internal data. I'm guessing those new duplicates are being used when they shouldn't be or are setup wrong. Regardless, they are not deconstructable (though they are minable). Interestingly, trees that you generated by planting trees (even with a blueprint) are not messed up and can be deconstructed normally (though they do behave slightly differently from normal trees). In the end I have no real idea.
I did fix the issue for my save file, however. Though it doesn't allow me to keep using tree blueprints. I created a mod with a migration json file to replace the blueprint trees with normal trees. Then I enabled that mod, disabled Blueprint Trees and then loaded my save file. This causes the trees to be fixed and as long as you leave Blueprint Trees disabled new trees generate correctly. I did like the mod though so I'm sad I can't use it.
If you want to try this, here is the migration json. You can create an otherwise empty mod to put it in. I followed the instructions here to build an empty mod: https://wiki.factorio.com/Tutorial:Modding_tutorial/Gangsir#The_tutorial_mod
{
"entity":
[
["BlueprintTrees-tree-01", "tree-01"],
["BlueprintTrees-tree-02", "tree-02"],
["BlueprintTrees-dead-dry-hairy-tree", "dead-dry-hairy-tree"],
["BlueprintTrees-dead-grey-trunk", "dead-grey-trunk"],
["BlueprintTrees-dead-tree-desert", "dead-tree-desert"],
["BlueprintTrees-dry-hairy-tree", "dry-hairy-tree"],
["BlueprintTrees-dry-tree", "dry-tree"],
["BlueprintTrees-tree-desert-b", "tree-desert-b"],
["BlueprintTrees-tree-desert-c", "tree-desert-c"],
["BlueprintTrees-tree-desert-f", "tree-desert-f"],
["BlueprintTrees-tree-desert-g", "tree-desert-g"],
["BlueprintTrees-tree-desert-h", "tree-desert-h"],
["BlueprintTrees-tree-desert-i", "tree-desert-i"],
["BlueprintTrees-tree-desert-j", "tree-desert-j"],
["BlueprintTrees-tree-desert-k", "tree-desert-k"],
["BlueprintTrees-tree-desert-m", "tree-desert-m"],
["BlueprintTrees-tree-desert-n", "tree-desert-n"],
["BlueprintTrees-tree-dryland-b", "tree-dryland-b"],
["BlueprintTrees-tree-dryland-c", "tree-dryland-c"],
["BlueprintTrees-tree-dryland-e", "tree-dryland-e"],
["BlueprintTrees-tree-dryland-f", "tree-dryland-f"],
["BlueprintTrees-tree-dryland-g", "tree-dryland-g"],
["BlueprintTrees-tree-dryland-h", "tree-dryland-h"],
["BlueprintTrees-tree-dryland-j", "tree-dryland-j"],
["BlueprintTrees-tree-dryland-k", "tree-dryland-k"],
["BlueprintTrees-tree-dryland-l", "tree-dryland-l"],
["BlueprintTrees-tree-dryland-m", "tree-dryland-m"],
["BlueprintTrees-tree-dryland-n", "tree-dryland-n"],
["BlueprintTrees-tree-grassland-b", "tree-grassland-b"],
["BlueprintTrees-tree-grassland-c", "tree-grassland-c"],
["BlueprintTrees-tree-grassland-d", "tree-grassland-d"],
["BlueprintTrees-tree-grassland-e", "tree-grassland-e"],
["BlueprintTrees-tree-grassland-f", "tree-grassland-f"],
["BlueprintTrees-tree-grassland-g", "tree-grassland-g"],
["BlueprintTrees-tree-grassland-h", "tree-grassland-h"],
["BlueprintTrees-tree-grassland-h2", "tree-grassland-h2"],
["BlueprintTrees-tree-grassland-h3", "tree-grassland-h3"],
["BlueprintTrees-tree-grassland-i", "tree-grassland-i"],
["BlueprintTrees-tree-grassland-j", "tree-grassland-j"],
["BlueprintTrees-tree-grassland-k", "tree-grassland-k"],
["BlueprintTrees-tree-grassland-l", "tree-grassland-l"],
["BlueprintTrees-tree-grassland-m", "tree-grassland-m"],
["BlueprintTrees-tree-grassland-n", "tree-grassland-n"],
["BlueprintTrees-tree-grassland-o", "tree-grassland-o"],
["BlueprintTrees-tree-grassland-p", "tree-grassland-p"],
["BlueprintTrees-tree-grassland-q", "tree-grassland-q"],
["BlueprintTrees-tree-palm-a", "tree-palm-a"],
["BlueprintTrees-tree-palm-b", "tree-palm-b"],
["BlueprintTrees-tree-snow-a", "tree-snow-a"],
["BlueprintTrees-tree-wetland-a", "tree-wetland-a"],
["BlueprintTrees-tree-wetland-b", "tree-wetland-b"],
["BlueprintTrees-tree-wetland-d", "tree-wetland-d"],
["BlueprintTrees-tree-wetland-e", "tree-wetland-e"],
["BlueprintTrees-tree-wetland-f", "tree-wetland-f"],
["BlueprintTrees-tree-wetland-g", "tree-wetland-g"],
["BlueprintTrees-tree-wetland-i", "tree-wetland-i"],
["BlueprintTrees-tree-wetland-j", "tree-wetland-j"],
["BlueprintTrees-tree-wetland-k", "tree-wetland-k"],
["BlueprintTrees-tree-wetland-m", "tree-wetland-m"],
["BlueprintTrees-tree-wetland-n", "tree-wetland-n"]
]
}
Maybe all this will help someone.