No, Ayurveda does not regard protein-rich food as dangerous for health. Being an ancient science, its focus is on natural supplements. Let me explain some fundamental concepts of Ayurveda.
In Ayurveda, the body and its diseases are products of food. Food is categorized as wholesome and unwholesome. Foods should be compatible with the body. Ayurveda lays great stress on selecting food, processing, cooking and has defined rules for healthy eating.
They also believe that nutrition is accomplished only when the inner biological fire system (Agni) and the inner transport system (srotasmi) are in order. I would interpret this to mean an emphasis on balancing the desire for food consumption and the associated digestive processes.
Ayurveda insists that diet is linked to nature and environmental conditions. Diet should be in tune with the individual personality (Prakriti), adverse personality traits (Vikriti), dosha, and body type.
Dietary supplements for the restoration of the body from the disease are also used in Ayurveda. Supplement treatment is called Rasayana therapy. Rasayanas are essential nutraceuticals. These help build the immune system, maintain mineral bio balance, provide essential nutrients, and possess antiaging properties.
Ayurvedic nutraceuticals or rasayanas could be tissue- and organ-specific. Thus, there are specific nutraceuticals for the heart, skin, brain, etc. They are also specific to the age of the individual and are also disease-specific. These are to be aligned with the digestive system and metabolism of an individual.
Twelve food categories are listed in Ayurveda. These are corn, wines, pulses, water, meat, milk and milk products, vegetables, sugar cane and related products, fruits, cooked products, greens, and food adjuvants. As you note, it contains both plant-based and dairy-based protein-rich foods.
The food should be appropriately cooked and processed, adaptable, and appropriate to individual requirements. Diet is aligned to an individual’s dosha.
According to Ayurveda, diet plays a role in keeping the mind healthy. They have classified three types of diet—the Sattvik diet, vegetarian, nonoily, and nonspicy. Rajasik diet is spicy, hot, sour, salty, and excites the mind, while the Tamasik diet is oily, heavy, and brings in lethargy.
There are contradictory diets that are indicated in Ayurveda. For instance, fish and fish products and milk, milk or milk products and alcohol, radish with milk, lotus stem with honey, or honey with clarified butter are not recommended to be taken together.

Additional reading:

Natural Solutions for Obesity, Cancer, and Diabetes ( A tri-series)

Asian Herbs and their wondrous health-giving properties

Holy Herbs; Modern Connections to Ancient Plants

Nutrition Facts: A guide to good health

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