If you really want to use a remote node, this can be done as well, but you have to consider everything possible for minimizing privacy-related risks. Long story short, the best way to anonymously use a remote node is to use Monero with TOR or with any other trustable VPN service.
What is TOR?
TOR is a free software that enables anonymous communication. The name of the program comes from the original software project name, The Onion Router and it’s an acronym for it.
TOR directs Internet traffic via a free, worldwide, volunteer overlay network that includes more than 700 relays that will conceal a user’s location and usage from anyone who is conducting network surveillance or traffic analysis.
While you are using TOR, it will be more difficult to trace your Internet activity, including your crypto operations. TOR’s primary purpose is to protect the personal privacy of its users as well as their freedom and ability to perform confidential processes by keeping their Internet activities from being monitored.
TOR encrypts the data, including the next node destination IP address, and does this multiple times. After that it sends it through a virtual circuit comprising successive, random-selection TOR relays. Each relay will decrypt a layer of encryption in order to reveal the next relay in the circuit to pass the remaining encrypted data on to it.
The last relay decrypts the innermost layer of encryption and sends the original data to its destination without having to reveal or know the source IP address.
Overall, this method eliminates any single point at which the communicating peers can be determined via network surveillance that relies on being aware of its source and destination.
So, as a conclusion using a Monero remote node that supports TOR might be the best solution for you if you don’t want to use your full node because this addresses the privacy-related issues.