People thought that BTC would be treated like gold. Where it would act in opposition to the stock market. If you ignore all the terminology and equations, then you can focus on the behavior of the investors. If investors buy, sell, and perceive BTC as a type of stock, then it will behave as stock. As inflation occurs, it will project into the crypto market via speculative investment.
The "inflation proof" concept of bitcoin is that there is a fixed supply. So, monetary inflation cannot occur within the currency itself. However, in the context of the larger financial market, it will be affected by systemic inflation.