I seem to recall we’ve been over this before.

Elections are handled in the states. The people who are responsible, in a given state, to determine whether someone is qualified to hold office are the ones who make that determination - whether the disqualification comes from Article II of the US Constitution (where the criteria for POTUS qualification are described) or from the 14th Amendment to the same US Constitution.

If someone feels they have been wrongly disqualified - regardless of why they were disqualified - have recourse to seek relief from that condition through state courts (and possibly federal courts, since it’s in the area of constitutional law, but I have other thoughts on that). Or, in the case of 14A S3, for each house of the US Congress to remove that disability each by a two-thirds vote.

In your example, if someone becomes disqualified from the ballot for being at a BLM protest, based on 14A S3, they would seek relief in one of those ways. And I would bet that they would be immediately successful, because BLM protests were not attempting to subvert the federal government, or interfere with the legal operation of federal government official business.