Politicians and the Eucharist

How is it that those politicians who openly support abortions can receive Eucharist?

The answer, while complex, boils down to two canon laws and how they are interpreted.

Can. 915 Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others obstinately persevering in manifest grave sin are not to be admitted to holy communion.
Can. 916 A person who is conscious of grave sin is not to celebrate Mass or receive the body of the Lord without previous sacramental confession unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition which includes the resolution of confessing as soon as possible.

The first deals with a juridical act by a bishop or other ecclesial authority. If a person’s bishop, (a) which is determined by his or her domicile, (b) or the pope, or (c) a given bishop exercising authority in his own diocese, (i.e., apart from the person’s diocese of domicile), regarding a grave public sin has formally stated that someone may not be admitted to Holy Communion.
The second deals with the conscience of a person. This is a determination of a person and his or her confessor regarding grave sin.

As you can see there are two distinct issues.
The first deals with a formal state of Excommunication, which is proclaimed and enforced by a bishop with competent authority. This would be similar to a secular judge in making the official declaration that someone guilty of DUI homicide loses the right to possess a driver’s license or to drive a motor vehicle.
The second is like a person who knows he or she is an alcoholic making a choice to not possess a driver’s license or drive a vehicle. For example, I know of alcoholics who rather than tempt themselves purposely have chosen to not get a driver’s license or own a motor vehicle.

A local priest, with certain exceptions, does not have jurisdiction or authority to refuse someone presenting themselves for Communion, unless the local bishop, or other bishop with competent authority, has declared such. It is important to remember that, while such behavior may cause scandal, Excommunication is an ecclesial discipline calling someone to repent, not a political issue. We are free to disagree with the local bishop, regardless, it is his call not ours.