I suggest that the two web entities use separate account systems. They are functionally independent of each other. One of them is actually hosted on salesforce while the other is by tableau software.
I use my work email to access custom.tableausoftware.com and use my gmail to access the community site. To me they are two different entities. One is for work and the other is for personal. Tying them together is not good.
However, I am forced to log out one when accessing the other. How about the server lets me stay logged in on both sites? It will make my life easier if using two different credentials to access them. And do not assume that people access them using the same credential.