Goal 1: access certain "anonymous" sites that you don't want to provide your real identity, IP or location to.
Goal 2: access "regular" sites that do require or have your real identity, such as your bank or Facebook.
All sites use end-to-end encryption over HTTPS, so packet sniffing isn't an issue.
Let's say you're using a VPN that you trust to not keep logs, and is located in a jurisdiction outside of the Five Eyes. Unless you use split tunneling, all your traffic will go through the VPN - both to regular and anonymous sites.
Is it a bad idea to access over the same VPN both sites that know your real identity and those that don't? What kinds of attacks could expose your identity to a) the anonymous sites, b) the attackers?
If one of the "regular" sites is subpoenaed, they can hand over your IP as well as the IP of the VPN(s) you've used to connect to them, but if you trust your VPN provider to not keep logs, this doesn't seem like a problem. If an anonymous site is subpoenaed for all users who've connected from that VPN IP, you have plausible deniability, since the VPN's external IPs are shared.