Based on what I have been told by my non-Kaiser physicians, you may wish to consider the following:
Mammograms are a must, once you reach a certain age. But for MtF, it is not your chronological age that counts, but the age of your boobs -- how long you have had them. If you are in a high-risk group (blood relatives who had breast cancer before age 60), start at 25 years. If normal risk, you can wait to 35 years. After that go annually.
You should be able to judge your prostate health through a PSA count during blood tests. As the treatment for an enlarged or cancerous prostate is estrogen, if you are on HRT the likelihood of prostate cancer are minimal, at best. Unless your PSA count is above 6, or shows a steady rise over the years, you can consider a prostate exam as optional. Even if you were to have a problem, most prostate cancer patients, even of untreated, die of something else first. The anxiety about prostate problems is that if can affect male sexual functioning -- something you no longer need to worry about, at least for yourself.
Bottom line, however, is that Kaiser is a HMO. As such, they gain nothing by having you do unnecessary tests; it costs them money. So if your specialist physician says you need a test, then you do.