In this situation, are you allowed to continue driving without stopping before the pedestrian crossing?

In the video you are driving along a forest road and approaching a pedestrian crossing with a cycle crossing, marked with sign D-6b; from the right, a person carrying a skateboard in their hand is stepping onto the crossing. You are not allowed to continue without stopping before the crossing. The answer is: no.

The Road Traffic Act requires a driver approaching a pedestrian crossing to exercise particular caution, to reduce speed and to give way to a pedestrian who is on the crossing or stepping onto it; giving way means holding back from moving if your movement could force the pedestrian to stop, slow down or walk faster. A person carrying a skateboard is a pedestrian - only when riding it would they be a user of a mobility aid. As they are stepping onto the crossing, driving over it without stopping would force them to step back or walk faster, which is exactly what is prohibited. So you stop before the crossing, wait until the pedestrian has crossed your lane and moved away, and set off while also looking at the cycle crossing next to it, where cyclists have right of way. On a forest road with no buildings, only the signs and the stripes remind you of the crossing - that is why you read them well in advance.

Legal basis: Art. 26 para. 1 and Art. 2 point 18 and 23 of the Road Traffic Act (Prawo o ruchu drogowym); § 47 para. 3 and 4 of the Regulation on road signs and signals