How to present the final model (e.g. random forest)?
The probability threshold can be changed and you would obtain different results for accuracy / recall / precision / F1 score (the objective). You could see this as an aspect of the parameters you have tuned to obtain the best objective.

Similarly for CV, the out-of-training fold objective would be reported together with the other parameters, such as number of trees and predictor subset size. One reason I could think of regarding the instability of threshold across CV folds is that the CV folds were not split up using stratified sampling, resulting in different proportions of positives observed across the folds.