Of course you have to pay attention to your own details, including your risk tolerance - yet in many circumstances if you wait to build up your emergency fund and back up funds first it could take you many months or even a year or more to get to a point that you are starting to feel that you have good back up funds..

Let's presume a very large number of people who do not invest live paycheck to paycheck, so maybe they ONLY have around 2-4 weeks worth of cashfloat that might be considered a kind of emergency fund, yet if you have no investment that you are trying to protect (such as bitcoin) then there is less to lose if you run our of your back up money, float, so part of the reason for having any extra buttress from regular people who do not tend to invest is because there is a desire to protect your bitcoin investment, and since bitcoin might be more volatile than other kinds of investments, there is more reason to protect that you do not sell any of it that is not completely at a time of your own choosing.... so yeah, part of the question may well become the extent to which you are protecting an investment (such as bitcoin), and if you are ONLY able to invest $10 to $100 into bitcoin per week, then your bitcoin investment is surely going to take a long time to grow to any significant size, and maybe it would take you 6 months or more to build your emergency fund if you were not investing into bitcoin, but perhaps if you build  your bitcoin and your back up funds simultaneously, it might take you 12-18 months or more to get them into a state of good order...

Each of us needs to decide - yet from my own point of view, I believe that it is way too overly conservative to be building your back up funds prior to getting started in bitcoin.
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When I started my Bitcoin accumulation journey I had a little savings which I converted to my back up funds, however it was not much or enough but when you talked about building one's emergency funds or back up funds along side his or her Bitcoin investment I started reflecting on it and I decided to try it just some days ago and is going well.
There's one thing I have discovered when it comes to bitcoin investment if you want to be successful you need to have a strong emergency, reserves and float funds which are your back up funds and if you have already started your Bitcoin investment if possible to still building up your back up funds a long side your Bitcoin investment all one needs to do is cut down his Bitcoin accumulation percentage in other to also accumulate his back up funds and that's what I just did when am done accumulating my back up funds then I can be a little aggressive in my Bitcoin accumulation.

Without a strong back up funds one will always find him self dipping his or her hand to his Bitcoin investment and that is why the main reason of building a strong back up funds is to protect one's Bitcoin investment, a lot of people feels it won't be possible building one's Bitcoin investment and back up funds together is very much possible just plan yourself very well and you can do it, so no need waiting for your to build your back up funds before starting your Bitcoin investment since you can do it together successful by giving a percentage that will be okay for you to each weekly or monthly.