Is it possible to invest in a bitcoin startup/company without being an accredited investor? Say for example I would like to invest in coinbase.com, is this possible?
Yes it is possible, though I highly doubt that you would be able to invest in a coinbase round without being an accredited investor with lots of experience in the bitcoin space. That's not because of legal requirements, it's just where they're at in their business. As a general rule though, anyone can invest in a startup if they're able to convince the existing controlling shareholders to allow it.
If you want to invest in the whole Bitcoin ecosystem, it's best to just invest in Bitcoin itself. This would essentially let you invest in the success of all Bitcoin companies, due to the limited supply of Bitcoin.
There are some companies that put their shares up in open marketplaces like Havelock. This would allow you to invest in some companies specifically.