The answer to your question is no - Snapchat messaging does not affect Best Friends.
This is according to Snapchat's own support page, which can be found here
Why Snapchat messaging doesn't directly impact "best friends"
Snapchat's support blog suggests that your 'Best Friends' represent the "friends you snap with most frequently and are selected automatically by a magical Snapchat friendship algorithm."
Your "Score" is the total number of Snaps you've sent & received.
Since messaging does not count as a 'snap', it is not included in your total score, therefore it does not affect your 'best friends' list.
Why is Snapchat's best friend algorithm design this way?
Apparently, this algorithm is designed to determine the snaps exchanged between both parties, not just those sent out by yourself. Snapchat then creates a list to display the total score of your most frequent exchanges - only via snaps, not messaging - in ascending order.
This is your best Best Friends list.
This means technically, even if you frequently receive snaps from a certain person, and you only respond here and there, they may still show up in your Best Friend list. This may be why you could be slightly confused over who is in your Best Friends list and why!
In summary, two parties messaging each other via text, without any snaps involved (which accumulate points) should not in any way affect your snapchat score which ultimately affects your Best Friends.
I hope this helps.
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