I imagine this would be different for different animals but to what extent does inbreeding affect the evolution of populations that have been isolated?

The answer is indeed different for different animals so hard to answer this in any quantitative way. However, in basic terms inbreeding (mating among relatives) is more likely to occur as populations become smaller and more fragmented (with reduced dispersal among sub-populations).

Often, but not always, inbreeding results in "inbreeding depression" which is a loss of evolutionary fitness (i.e. higher mortality risk and/or lower reproductive output). This happens because recessive deleterious alleles are more likely to come together in the homozygous state (so that the deleterious effecs are felt) in the offspring of related parents. The amount of inbreedfing depression in a population is therefore dependent on 1) the amount of inbreeding and 2) the load of deleterious mutations in the population. Both of these factors vary a lot among different animal populations.