OOB error will give a misleading indication of performance on a time-series dataset because it will be evaluating performance on past data using future data. This does not give a good indication of the model's ability to perform on future data. Therefore, use a methodology like TimeSeriesSplit.
By holding out future data points for model evaluation, you examine your model's ability to perform in the future. To build your intuition on why it's "cheating" to evaluate your forecasting ability using future data points: suppose I ask you to predict my weight a year from now, given measurements I took over the past 365 days. That might be challenging, unless you see a clear pattern. Now suppose that I ask you to predict my weight on day 155 of the 365 days I already recorded, and all I do is hold out day 155. You could easily estimate my weight as (w + w) / 2. You just took the average of the weights between two days. But did you forecast the future? (No.) Does a measurement of your success imply you can predict my future weight? (Certainly not!)