A stranger passing Filipinos who are eating will automatically be invited to "come and eat." It's polite to say you've already eaten. If people insist, or if there's an abundance of food such as at a wedding or fiesta, then by all means participate. Don't accept the first invitation. It's better to point out how inconvenient it would be for the host, or to make a polite excuse, then wait to see if you're pressed further. It's the Filipino way, enabling the visitor to gauge whether an invitation is genuine or not.
Travelers should always take into account the reverence Filipinos have for food. Regular mealtimes are strictly observed. When visiting a home, you'll be offered food and drink. It's polite to wait to be urged to sit at the table or begin eating. If you don't like the food, eat a little and make an excuse rather than reject it outright. Guests leave a little food on the plate to indicate they're satisfied.