Should random forests based on same data but different random seeds be compared? I know that if you re-run a random forest with a different random seed you will fit a different model. I'm wondering whether it's acceptable to compare different random forest models (run under different random seeds) and to take the model with the highest accuracy on the training data (using 10-fold CV) for downstream work.
As an example, below is the distribution of accuracies based on 10-fold CV in a dataset with 147 samples and 278 features (all two class features) used to predict disease state (two classes: healthy / diseased). This distribution is based on 100 RF replicates with different random seeds: 

Is it wrong to take the model with the highest accuracy for feature selection and to fit my test data? 
I'm also interested in comparing the chosen model's 10-fold CV accuracy to additional RF models' accuracies fit to the same dataset with randomized disease states (as an alternative way to evaluate significance since I think my sample size might be too small to split it into test/training data). I'm concerned that this approach might be biased if I choose the model with the highest accuracy.
 A: Random Forest converges with growing number of trees, see the Breiman 2001 paper. So if you would set the number of trees (ntree) to infinity, you would always get the same accuracy (or some other measure like logloss). It only varies a lot because your number of trees is too small (or your resampling strategy (10-fold-CV) is to unstable, can be reduced by more repetitions). 
In normal data situations (especially if the data is big enough) your accuracy should grow with growing trees. So instead of training with 100 different seeds I would train one randomForest with actual_ntree * 100 or even more. 
In some packages you can also see the development of the accuracy with growing number of trees. 
For getting a faster evaluation and possibly tuning you can use out-of-bag estimations, that are usually implemented in standard packages (like randomForest in R). They are normally as good as 10 fold-CVs (and more stable) if the number of trees is big enough. 
A: Accuracy is just another random variable that depends on your model, the seed, the train / test split, quality of your current data etc. - maximizing this random variable does not automatically lead to the best possible generalization of your model. 
Besides looking at metrics like accuracy, logloss, auc roc etc. you might also want to look at other learning characteristics like the learning curves of your train / testdata while adding more data, the difference between the train and test error etc., as finally all you are facing is the bias-variance-tradeoff that lives in every model.
See https://en.m.wikipedia.org/wiki/Bias–variance_tradeoff
To answer your question, you should not only rely on comparing the random seed. 
