I did a brief search this morning and managed to track down at least some of the literature on the effect of second language immersion on reading acquisition. I'm sure there's much more than I found, and I can't guarantee I am reporting the consensus view. But the papers I looked at generally seemed to agree that there is no harm at all to letting your kids learn to read in their first language at home at the same time (or even before) they are learning to read in the immersion language at school. A lot of the research seems to have been done in Canada, since there are a lot of state supported French immersion schools there attended by native English speakers. (You can imagine the political hot potato that one must have become.) One of the papers does report that for kids who begin French immersion in K, their English reading skills in 1st and 2nd grade are a bit behind those of peers in English only schools. But this is not so surprising, since English reading is not taught in 1st or 2nd grade in the French immersion schools. When English reading instruction begins in 3rd grade, however, they catch up and often even surpass their English-only peers. (This paper is in Reading Research Quarterly and is called "English Reading Skills of French Immersion Students in Kindergarten and Grades 1 and 2". It is probably not the latest word, since it was published in 1987.)
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