Islamists has nothing to do with it.
Truly, from the Philippine point of view Islamism is a secondary issue. Islam is a very minority religion there (less than 6%) and nearly entirely restricted to a mostly isolated region. It is a noisy business but - and this is often missed - this has been a cause of trouble for 400 years. Not a new thing, this is so old that artifacts of the conflict are subjects for archaeology.
The very small Philippine armed forces has that as their main problem but it is scaled to the resources being applied.
The Muslims are annoying.
The Chinese are frightening.
Far more important to the Philippines are the economy and the strategic issues of great power rivalries. The US is perceived as weak or unwilling and not to be relied on in a confrontation with China.
As far as Obama is a supporter of same, they become far greater of a factor, albeit not a direct factor on Philippine soil. It goes along with Obama projecting US weakness, which you mentioned.
Islamists has nothing to do with it