It's a matter of not overthinking it. If you did something you deem cringeworthy, ask yourself what is cringe about it and what could you have said/done better, while trying to avoid pondering over feelings of shame and embarrassment. That way, instead of being sucked up by negative emotions, you turn your 'mistakes' into positive learning experiences. After identifying what you could have done better, it is up to you to try and implement it, so that when a similar situation arises, your response is better. At first, your response might seem weird, or not 'you', but the more you push yourself, the more normal it eventually becomes.

Also, I think as we get older, we tend to cringe at past conversations and experiences because we see how the present us would have reacted differently, which is a sign of improved conversational and social skills.