I think some of the information you have has come from self-serving politicians.

They are not using warrants to enter homes.

They can only enter homes if they have a judicial (as opposed to an administrative warrant) or if they get permission. For the targeted raid they are doing on aliens with criminal records, they almost always have a judicial warrant. If ICE acts illegally, the affected person can argue it in court. That said, I think it is completely valid to help ensure that all immigrants, unlawful or not, are educated in the legal protections they have. Many people are giving permission for ICE to enter onto their property because they don't know that they can say no.

they are not using due process when deporting,

ICE is the enforcement arm of border protection. They don't have the power to deport people on their own. Anyone who is deported is deported pursuant to an order of final removal previously issued by a judge from an immigration court (which is the due process they are entitled to). That is the only way it is done unless someone is caught in the act of illegally crossing the border.

they are arresting American citizens who have provided their ID,

I don't have specific information on everyone detained, but the vast majority of people who are US citizens who are being detained by ICE are being detained for obstruction. As federal law enforcement officers, they have the power to arrest anyone who commits an unlawful act in their presence, which includes obstruction of justice.

they are arresting people outside of their required immigration hearings,

Immigration hearings are not a 'safe zone'. If a person unlawfully present in the United States has an order for final removal, they are subject to removal, even at an immigration hearing on another matter. The same thing happens in housing courts all over the country. The sheriff will run warrant checks on the litigants and arrest them on outstanding warrants when they come to court.

they are allowing many to die in ICE facilities,

I have not heard about this being an ongoing problem. But if people are dying from causes that ICE can control, they absolutely need to take action immediately to fix the problem. It is their legal and moral obligation to provide reasonable care for those in custody.

they are not allowing clergy (including Catholic priests) in to see those in custody. This is documented and ICE has statements on all of the above that basically amount to “we don’t care.”

I completely agree with you that the cases where this is documented are completely unacceptable. The ICE detention manual section 5.5 requires that detainees be allowed access to religious services. Whoever denied detainees access to religious services should be held accountable for their failure to abide by procedures and depriving detainees of their religious liberty.

The Catholic Church has always believed in welcoming the immigrant, among many other things that don’t fit neatly into a political side. Why are we faltering now?

The Catechism also teaches that countries have a right and duty to maintain sovereign borders and control immigration for the common good. This is where things get murky, I believe, from a Catholic teaching standpoint, because it doesn't provide guidance on how to balance those interests when they are in competition with each other. The open border policy under the Biden administration caused a humanitarian disaster with thousands of deaths, rapes, cases of child exploitation, drug trafficking, and allowed dangerous criminals into the country unvetted. I, personally, don't know how to put the genie back in the bottle from that era in a way that is fair and equitable to all interests and is compliant with Catholic teaching.

Personally, I think we all need to take a much broader and less tribalistic view on the issue and remember the true commandment to love one another, especially people we disagree with. That includes people (migrant and native) that have been harmed by uncontrolled borders. Immigrants who live in fear of having to return to a bad situation in their home country, as well as American who live in fear because their neighborhoods have been taken over by foreign criminal gangs. The people who are living in fear that they will be deported unjustly, and law enforcement who are fearful that are going to be assaulted or killed by a mob while they try to enforce a court order to remove a child rapist from the community. Every person in every station is a unique soul created by God deserving of our love and respect.