First, an important fact about non ionic detergents- {1}They have a hydrophilic head group that is uncharged and are preferred for their ability to break lipid-lipid and lipid-protein interactions. They have limited ability to break protein-protein interactions and are often referred to as non-denaturing detergents and are used to isolate biologically active membrane proteins.
Generally, moderate concentrations of mild (i.e., nonionic) detergents compromise the integrity of cell membranes, thereby facilitating lysis of cells and extraction of soluble protein, often in native form.
An example would be Triton X-100. {2} Non-denaturing detergents such as Triton X-100 have rigid and bulky nonpolar heads that do not penetrate into water-soluble proteins; consequently, they generally do not disrupt native interactions and structures of water-soluble proteins and do not have cooperative binding properties. The main effect of non-denaturing detergents is to associate with hydrophobic parts of membrane proteins, thereby conferring miscibility to them.
The following article is about the same protein insolubility that I have written above, but in the nuclear membrane of chicken RBC’s. {3}
Protein has been selectively extracted from isolated chicken erythrocyte nuclear envelope by (1) dilute MgCl2/Triton X-100 followed by (2) concentrated MgCl2/Triton X-100 solutions. Certain proteins appear to be selectively dissolved in the first solvent and may occur in the nuclear envelope primarily as lipoproteins. 171
Among the proteins insoluble in the low MgCl2/Triton X-100 wash, as well as in 500 mM MgCl2 without Triton previously used in the preparation of the envelope fraction, the quantitatively major polypeptides dissolve in a combination of high MgCl2 and Triton X-100. Further, much of this dissolved protein precipitates when the MgCl2 concentration is lowered by dialysis. The insolubility of these proteins appears to result from a combination of ionic and hydrophobic interactions and may explain the resistance of nuclei to various manipulative procedures including nonionic detergent washes.
The conclusion is that the protein insolubility of these detergents is what makes the nucleus resistant. You know that the phospholipid bi-layer is common for both- the cell membrane and the nuclear membrane. But underlying the inner nuclear membrane is the nuclear lamina, a fibrous meshwork that provides structural support to the nucleus. The nuclear lamina is composed of one or more related proteins called lamins.
Coming to your last question, using the example of Triton X-100 and leukocyte cells, a paper says: {4}
Leukocyte membranes except the nuclear envelope were solubilized in a buffer that contained 1% Triton X-100.
Which means that all membranes- including mitochondrial, dissolve in the detergent because they do not have an additional protein layer in them, like the nucleus does.
1-http://www.genotech.com/protein-research/detergent-accessories.html
2-https://www.thermofisher.com/in/en/home/life-science/protein-biology/protein-biology-learning-center/protein-biology-resource-library/pierce-protein-methods/detergents-cell-lysis-protein-extraction.html
3-https://pubmed.ncbi.nlm.nih.gov/999948/
4-https://link.springer.com/article/10.1007/BF00554425 171