If you're strict or allergic, very difficult. Fish sauces and pastes like terasi and patis are culinary staples on the level of soy sauce and make it into otherwise seemingly vegetarian dishes.

If you're willing to flex a bit and just avoid obvious meat/fish, you'll survive, there's plenty of tofu, tempeh, veg etc. Gado-gado is always veg, nasi/mee goreng, etc.

Tempeh is an Indonesian staple and from what I understand pretty popular with vegans.