Here's my Python3 implementation in analogy to MatLab's imreconstruct algorithm:

import cv2
import numpy as np


def imreconstruct(marker: np.ndarray, mask: np.ndarray, radius: int = 1):
    """Iteratively expand the markers white keeping them limited by the mask during each iteration.

    :param marker: Grayscale image where initial seed is white on black background.
    :param mask: Grayscale mask where the valid area is white on black background.
    :param radius Can be increased to improve expansion speed while causing decreased isolation from nearby areas.
    :returns A copy of the last expansion.
    Written By Semnodime.
    """
    kernel = np.ones(shape=(radius * 2 + 1,) * 2, dtype=np.uint8)
    while True:
        expanded = cv2.dilate(src=marker, kernel=kernel)
        cv2.bitwise_and(src1=expanded, src2=mask, dst=expanded)

        # Termination criterion: Expansion didn't change the image at all
        if (marker == expanded).all():
            return expanded
        marker = expanded

The morphological opening is ideal for this problem. It removes all the white parts thinner than a given diameter.

In OpenCV it is implemented in cv2.morphologyEx using op=cv2.MORPH_OPEN:

kernel = cv2.getStructuringElement(cv2.cv.MORPH_ELLIPSE, diameter)
output = cv2.morphologyEx(image, cv2.MORPH_OPEN, kernel)

But note that this removes parts of objects that are thin, it doesn't leave the full object if a part of it is wide enough. That can be done using an opening by reconstruction, an erosion followed by a morphological reconstruction (also known as geodesic dilation).

OpenCV doesn't have that algorithm. This Q&A gives a rough outline for how to implement it in OpenCV, but that is a very expensive algorithm, there are much more efficient ones.

There might be an implementation in Scikit-image, I haven't looked for it.

DIPlib (with Python bindings called PyDIP) (also, I'm an author) has a dip.OpeningByReconstruction. Install the Python module with pip install diplib.