RandomForestRegressor results are not reproducible

### Describe the bug

We use the ''RandomForestRegressor'' from ''sklearn.ensemble'' to produce estimates of conditional means. Despite setting a random seed, the estimated conditional means are not reproducible when we enable multiprocessing. For some observations, conditional mean estimates change when rerunning the same code. We use the ''RandomForestRegressor'' in our statistical analysis. The non-reproducibility in the predictions of the ''RandomForestRegressor'' carries over to our estimates. Below, we provide an example to illustrate our issue. 

### Steps/Code to Reproduce

```python
import pandas as pd
import numpy as np
from sklearn.ensemble import RandomForestRegressor

# %% Data

df = pd.DataFrame(
    [[4.0, 47.0, 0.0],
     [-3640.913, 35.0, 1.0],
     [-32622.293, 25.0, 0.0],
     [-92.50659, 22.0, 0.0],
     [1179.845, 20.0, 0.0],
     [8750.0, 37.0, 0.0],
     [3559.3333, 24.0, 0.0],
     [-4778.8965, 30.0, 0.0],
     [-16032.402, 61.0, 1.0],
     [520.00903, 36.0, 0.0],
     [4428.75, 48.0, 0.0],
     [9622.75, 53.0, 1.0],
     [5254.0076, 30.0, 0.0],
     [1688.47, 28.0, 0.0],
     [9.0, 60.0, 0.0],
     [22777.727, 51.0, 0.0],
     [200.0, 58.0, 0.0],
     [-4501.4166, 50.0, 0.0],
     [368.795, 22.0, 0.0],
     [20.0, 69.0, 1.0],
     [8858.34, 18.0, 0.0],
     [43.0, 22.0, 1.0],
     [93.0332, 29.0, 0.0],
     [5221.1133, 23.0, 0.0],
     [7197.25, 29.0, 1.0],
     [3250.36, 48.0, 1.0],
     [547.345, 47.0, 0.0],
     [27.0, 45.0, 0.0],
     [2306.2524, 18.0, 0.0],
     [8371.8335, 51.0, 0.0],
     [-7143.3364, 41.0, 1.0],
     [1435.5533, 37.0, 0.0],
     [-2594.5981, 25.0, 0.0],
     [43.0, 30.0, 0.0],
     [1260.3575, 48.0, 0.0],
     [-88.98999, 20.0, 0.0],
     [-22231.859, 50.0, 0.0],
     [-3400.951, 39.0, 0.0],
     [4192.92, 36.0, 0.0],
     [769.2666, 21.0, 0.0]])

# %% Parameters

NUMBER_OF_WORKERS = [1, 20]
NUMBER_OF_ROWS_TRAINING = 20
NUMBER_OF_ROWS_PREDICTION = 20
N_ESTIMATORS = 1000
MIN_SAMPLES_LEAF = 5
MAX_FEATURES = 1
BOOTSTRAP = True
OOB_SCORE = True
RANDOM_STATE = 42
rng = np.random.default_rng(9324561)

# %% Estimation

for workers in NUMBER_OF_WORKERS:
    for i in range(2):
        x_np = df.iloc[:, 1:].to_numpy()  # features
        y_np = df.iloc[:, :1].to_numpy()  # outcome
        regr = RandomForestRegressor(
            n_estimators=N_ESTIMATORS, min_samples_leaf=MIN_SAMPLES_LEAF,
            max_features=MAX_FEATURES, bootstrap=BOOTSTRAP,
            oob_score=OOB_SCORE, random_state=RANDOM_STATE,
            n_jobs=workers)
        regr.fit(x_np[:NUMBER_OF_ROWS_TRAINING, :],
                 y_np[:NUMBER_OF_ROWS_TRAINING, 0].ravel())
        y_pred_rf = regr.predict(x_np[NUMBER_OF_ROWS_PREDICTION:, :])
        if i == 0:
            y0 = y_np[NUMBER_OF_ROWS_PREDICTION:, 0] - y_pred_rf
        if i == 1:
            y1 = y_np[NUMBER_OF_ROWS_PREDICTION:, 0] - y_pred_rf
    print('Share of non-equal values using', workers, 'worker(s): ',
          np.mean(np.equal(y0, y1)))
```

### Expected Results

We would expect that - fixing a random seed - results should be reproducible. That is not the case. 

### Actual Results

Results are not reproducible. 

### Versions

```shell
0.24.2
```

COMMENT:
@glemaitre 
I observed the same behavior in version 1.6.1. 
Since  [#22303 (comment)](https://github.com/scikit-learn/scikit-learn/issues/22303#issuecomment-1023258329) and others need deterministic behavior could that please be mentioned in the docs. Otherwise one would assume setting the `random_state` is enough and run some extensive calculations  only to find out they are not reproducible when run in parallel.

Labels: Bug, Needs Triage