I agree that the Planned Parenthood Federation of America should not be taxed, because it's already taxpayer funded. Better just to remove all taxpayer funding from it. It's been around since the early part of the last century, and became a part of the International Planned Parenthood Federation in 1940s. But it was Nixon who signed into law the Family Planning Services and Population Research Act in 1970 which began federal funding of the organization. The law enjoyed bipartisan support from liberals who saw contraception access as increasing families' control over their lives, and conservatives who saw it as a way to keep people off welfare, both current and the as-yet conceived. Catholics didn't much like it, though.
But of course rather than giving families increased control over their lives and reducing the welfare rolls it has evolved into doing neither of those things, since from the very beginning of federal funding is was really and truly a backlash of the consequences of Women's Liberation, and has serviced far more single women than families, and has helped to increase the welfare rolls by encouraging even less personal responsibility than The Pill did (IMHO, of course). They get about one-third of their $1 billion revenue from the federal government in grants and contracts. None of that money goes directly to fund abortions, of course, but at the same time it certainly frees up other funds to be used for abortions, which is, in effect, the same thing. Not a penny of federal funds should be use to pay for (as per law), or to facilitate abortions, which is exactly what is happening by the federal money freeing up other money.
As for AARP, yeah, they should be taxed. They're a non-profit group, but only because their profits are funneled directly towards partisan political lobbying efforts. So their tax exempt status has taxpayers in effect paying for their lobbying efforts.
The twofold reasons churches shouldn't be allowed to engage in "First Amendment" partisan politics is the same that federal workers cannot, because it leads to corruption and a subversion of the democratic political process, because churches, like federally funded teachers, have undue influence over a captive audience who is primed to be led blindly and do as they are told, and they would be doing it, in effect, financed by taxpayer money.