What's not even mentioned in the article is that this could protect the entire Mediterranean coast line against rising sea levels[1].
[1] https://link.springer.com/article/10.1007/s11069-015-1821-8
[1] https://link.springer.com/article/10.1007/s11069-015-1821-8
I think a few existing coastal cities might object...
I live on a small island that's just above sea level and of course the main city and other towns are on the coast. We'd lose about 50% of the land here.
The strait is really narrow, with really strong currents and a huge change in salinity.
Not fun.
Probably they're not the only sea creatures that cross Gibraltar so this is a concern. Non a minor objection, but one among the many that would be raised. Think also about the political and military implications of a bridge from Africa to Europe.