Yes and no. Plenty of people care, just not in the countries that are emitting the most carbon. Lets take a look at the top 10 Google search regions on the right and their per capita carbon emissions from 2013. Fiji (1.9), Maldives (2.7), Australia (16.3), Jamaica (2.8), Puerto Rico (NA), Taiwan (10.3), Singapore (9.4), Philippines (1.0), New Zealand (7.6), Hong Kong (6.3). A huge proportion of searches in small island nations (which emit little carbon) are dedicated to coral bleaching. However, this is for the entirety of the 2004-2018 data. If you search by country, it appears that searches regarding coral bleaching have declined or have remained constant over the years, even in the midst of recent massive bleaching events.