No, I don't think she was a 'nutcase' or 'insane'. She has been very badly misrepresented throughout history by those wanting to put the blame on her shoulders for the downfall of the Romanov dynasty.
Alexandra was a shy, nervous person as a result of her upbringing. She was surrounded by death and grief, both at home, after the death of first her brother Frittie and then her mother and sister May, and also at her grandmother Queen Victoria's, where she often stayed. She rarely laughed after the death of her mother, and withdrew into herself and into religion. She was not suited to the role of Empress of the largest and richest empire in the world, and it didn't help that her mother in law Empress Marie was adored by the people and a much more outgoing and personable personality than herself.
So, firstly, she was under the immense strain of having to be the consort of an autocratic monarch, being on show the whole time and expected to live up to the example of her mother in law, who had a completely different personality to her. Secondly, she knew she was not liked at court and amongst the public, and her lack of skill in speaking French and Russian, the languages of court and the people, alienated her.
Thirdly, she was under intense pressure to produce an heir, which it took her ten years and four daughters to do. This made her even more unpopular amongst the public, and the family, as her sister in law Xenia managed to produce 6 strapping sons in the same time period. When her son was finally born, he suffered from an incurable and potentially fatal disease that she had given him, causing her to worry every day for the rest of her life over his health and the impact his death would have on the family and Russia as a whole.
Imagine being in that position. Plus, Alexandra suffered from constant (possibly psychosomatically induced) pain, which made her bedridden and depressed a lot of the time. She was deeply religious, and she believed that Rasputin would be able to help cure Alexei. Watching your son in such intense pain and not being able to do anything about it is going to do something to you, and unsurprisingly Alexandra turned desperately to whoever could help. When Rasputin appeared to ease Alexei's suffering, she latched on to him and would not listen to any of the damaging rumours circulating about him and his relationship with her.
The bottom line is, Alexandra had a very difficult life. She may have been rich and lived in opulent splendour, but she was forced into a public role she was not physically or mentally capable of fulfilling with ease, and she was also permanently worried over the health of her son. She was not mad, just a desperate woman looking for anyone who could help her son. Because the Russian public did not know about Alexei's illness, they jumped to the conclusion that Alexandra was having an affair. Also, her inability to run the state while Nicholas was away and trusting in Rasputin's advice rather than ministers is also used as 'proof' that she was mad. I prefer 'lacking in experience'. Alexandra trusted Rasputin because she believed in him and his powers, and I don't think she really had anyone else to turn to. Nicholas' family were not supportive of her, and she didn't trust the ministers because she thought they were conspiring against Nicholas and wanted to take away his absolute power.
People forget that Alexandra was a product of a closeted upbringing, a world where she was not needed to be practical or have knowledge of politics or policy. She knew nothing about the people of Russia or their needs; that is evident from her diary entries. She simply could not grasp or understand a life outside of her own. She lived in isolation at Tsarskoe Selo and anything that was unpleasant she simply pretended didn't exist. She wasn't mad, she was just didn't have enough knowledge of the real world to make her understand what was really going on. Her ignorance and desperation to help her son is what people construe as madness.
That's my opinion, anyway.