Does applying for Obamacare disqualify me from FEIE?

If you are a resident of Taiwan why would you want to have health care insurance that is only US based and has to be applied for using healthcare.gov - https://www.healthcare.gov/

To answer your question - No, having health care insurance from one of the US states under the one of the ACA plans does not disqualify you from being eligible for the Foreign Earned Income Exclusion.

I travel to US a few months a year, so either a travel insurance or ACA.  

I thought having a plan under ACA means I am an US resident which could potentially disqualify me from being eligible for FEIE.