Your question mixes up majority of population and freedom of religion in Indonesia.
Even if Indonesia has 86% Muslim, and Indonesia is the state with the highest muslimic poulation, it is NOT a muslimic state.
There is no established state religion, and therefore
the Garuda eagle and other symbols of Indonesia that are used
does not have to fulfil any muslimic/islamic rules like sharia etc.
Official there are six religions in Indonesia with same rights:
(Catholicism "Katolik", and Protestantism, "Kristen"
are recognised separately),
Even if Garuda may be a hinduistic symbol and the founders of the nation have agreed that this should be the heraldic animal, what does this has to do with 86% muslims if the country takes it freedom of religion serious? ;-)
Like Charle Evans answer is stating: "Apparently the Muslims participating in the selection process were satisfied, and thus Indonesia acquired its national emblem."
-> That's lived healthy cooperation between different religious groups.
For comparison, say, in Bangladesh, which has a similar
percentage of Muslims, I think it is unthinkable to
select a Hindu symbol as a national emblem.
It seems like Bangladesh is for you a "role model" of
holding up the islam.
In fact Bangladesh is one of the counties with the most violence against people of religious minorities like christians. (see link)
"Christian converts of Muslim, Hindu, Buddhist, or ethnic origin suffer the most severe restrictions in Bangladesh,"