Last week the U.S. Supreme Court ruled in Espinoza v. Montana Department of Revenue that when public funds (e.g. grants, aid, forgivable loans) are made generally available to any organization that meets certain neutral criteria, a religious organization that meets the criteria cannot be excluded merely because it is religious. The First Amendment's Establishment Clause requires the government to be impartial when it comes to religion, showing no preference toward any particular faith, or toward religious believers in general. But that doesn't mean that religious organizations must be barred from funding that is otherwise generally available.
So, assuming the Catholic parishes, dioceses, and organizations satisfied same the criteria for the PPP loans as everybody else, I don't think there's a "separation of church and state" issue here.
Another consideration: What happens if they were ineligible to participate in the PPP. They would likely be forced to furlough or lay off employees. Because churches don't pay into states' unemployment programs, those employees would not be eligible to collect unemployment insurance (or the federal government's additional unemployment aid), which would put them in pretty bad shape. I happen to think that churches SHOULD pay into unemployment programs or provide similar unemployment benefits for laid-off workers, but that's not the reality right now. And so having churches participate in the PPP is an available way for the government to look after people who happen to work for religious employers.
As for some of the more controversial details -- lobbying for special classification with regard to employee size restrictions -- I would not be surprised if the Church were in the wrong there, although it's certainly true that the Church has an organizational structure that far predates and doesn't map cleanly to U.S. corporate structures.