Investment according to Islamic law is not a sin and traders are encouraged to make a fair profit from business engagements. But collecting interest from loans which is called raba is prohibited according to the Holy Books of the religion. The question might be how Islamic banks make a profit. They make their gains through business partnerships or equity participation. This means that there is an agreement that allocates a certain percentage of profit from the business to the bank.

I don't think the Islamic religion is against investing in bitcoin or other cryptocurrencies but using bitcoin for loan services that require interest is not permitted and borrowing money with interest to invest in bitcoin might be against the Holy Book..