In the photo to the left, Korean protestors rip up a portraint of one of the Japanese lawmakers planning to visit the museum during a rally near the Japanese Embassy in Seoul. LINK
I think the reason Koreans are opposed to Japanese lawmakers visiting the museum is that they fear the lawmakers will expose some of the distortions and outrageous claims made at the museum, which is more of a propaganda facility than a real museum. The Korean government seems to be embarrassed by the museum. If Seoul were proud of the museum, then wouldn't the Korean government be encouraging the Japanese to visit the museum rather than discouraging them?
Probably one of the more infamous examples of the distortions at the Dokdo museum is an altered model of a 1530 Korean map. In the original map, an island labeled Usando (于山島 - 우산도) appears off the west coast of Ulleungdo (鬱陵島 - 울릉도), but in the model at the museum, Usando appears off the east coast of Ulleungdo. Koreans claim that Usando was the old name for "Dokdo," but Dokdo is off the east coast of Ulleungdo, so the museum staff apparently switched the location of the island on the model to better support their claim.
A copy of the original map and the altered model at the museum appear below: