Short answers: For real-time games, unacceptable. For correspondence it depends on specific rules, but is most likely acceptable.
First, such answers are always based under the rules of whatever venue you're playing at. Almost every venue has rules which address what resources you are entitled to, although some places are more clear about what is acceptable than others.
Almost every game played in real time has rules which essentially amount to your brain being the only allowable resource to use during the game. This is pretty much true of over-the-board and all internet servers. How much they can detect and enforce that differs from place to place. It is postulated, though, that this is the reason that 3 minutes plus 12 seconds increment has become the most popular time control for online games - a little too quick for help even for the weak-willed. (Though in the late 90s, some GMs like Garry Kasparov pushed for the idea of "assisted" or "advanced" chess at higher rated levels of play - essentially OTB games where the players are allowed real time computer engine assistance.)
In correspondence, the rules change radically. Most of them boil down to: You can't have human help, and you can't use a computer to analyze your game in real time to suggest the best line of play. However, you can use any form of book or database (precomputed) assistance. In a nutshell, you can use help from websites as long as that site isn't running a real time analysis from an engine to suggest your best move. (Or you're not posting on a forum, "Hey, here's my position, what's the best move?") Pre-computed analysis is acceptable most anywhere in correspondence. (Here I am using pre-computed as you didn't do or commission external analysis while the game is being played, but are looking up already published information. Whether a computer compiled the information or not.) This includes tablebases: They are acceptable most places, because it is precomputed - you are only querying a database.
These rules date from the era of tablebases being limited to things like KQK, KBBK, or KRRKR endings. As storage capacities of systems continue to increase (along with the massive bodies of chess knowledge being freely available,) the rules may once again evolve. For example, correspondence bodies which say that even real-time analysis is acceptable. I'm not aware of any which advocate, "You can't use any help at all during your game," because it would be unenforceable.
As database capacities continue to increase, we may eventually see a time where database analysis and engine analysis become close to identical.
Until then, the rule of thumb to follow is: In correspondence, did someone or something compute here-and-now what move I should make, or did that knowledge already exist? In real-time, use only your brain.
Good luck, and enjoy your chess!