Indeed. I also rarely "call out" someone when they engage in what's clearly a fallacious argument. Instead, I will engage by saying "I don't think that is an accurate portrayal of the position, because [..]" (strawman), "because [other thing] is bad doesn't say much about [this-thing]; if you want to talk about [other-thing] we can do that another time" (whataboutism), "Just because [organisation/person/group] says X doesn't mean X is true, I think it's more important to look at the arguments they're making" (argument from authority), etc.

This way it doesn't come off an an accusation, it keeps the conversation going, and is generally much more constructive. I found that people who "call out" logical fallacies and the like are generally looking to "win the argument" rather than actually have a conversation.

Calling people out on "bad faith" is common; there's an entire string of terms for this ("gaslighting", "sealioning", "concern trolling", what-have-you). I've never seen it end well. If someone is actually engaging in bad faith then it's better to disengage and call it a day, and if someone is engaging in good faith then all you've did is insult them without actually contributing all that much.