As I haven’t researched this super recently, these details should be checked out, but the general idea is definitely accurate:
This discussion (renouncing citizenship/ IDF service/ visiting Israel, etc.) appears to be involving individuals who do not live in Israel. An Israeli citizen (by virtue of being born in Israel, having an Israeli parent, etc.) is not obligated to perform his IDF service as long as his permanent residence is abroad. He/ She is allowed to visit Israel (there is a maximum amount of time per year that I don’t remember), and can spend 10 months ONE time as a student. However, you MUST follow all the rules and get the proper documentation. That includes an Israeli passport (and with the computerized records nowadays, there is a very strong chance they will know you are Israeli even if you try to enter on a foreign passport), and getting your official deferment from the Lishkat Hagiyus (Draft office). (This can be done through the embassy in the U.S.)
Religious girls are automatically exempt from army service (not simply a “deferment” which puts it off), so if you are a frum girl/woman, it may be worth it applying for that exemption rather than simply the non- resident exemption. You would have to prove that you are really religious, and they’ve gotten stricter about that lately, but if you really are, it shouldn’t be a problem.
My husband was born in Israel and moved to the US as a baby. He visited Israel numerous times, and even learned in yeshiva there, but was careful to keep his documents current.
If at any point you move to Israel (via official Aliyah or not), the deferment is no longer valid, and one would have to report to the lishkat hagiyus to determine what army obligations one has (dependent on many factors such as age, whether one is married with kids, job, etc.), and either perform the IDF service or get the appropriate paperwork for an exemption or further deferral.
BTW, renouncing citizenship can also have an effect on your kids, particularly if they ever choose to make Aliyah — it can impact their Aliyah benefits. Make sure to look into that as well before choosing to renounce their citizenship. (Obviously if you renounce your own citizenship before they are born, then this won’t apply as the won’t be citizens to begin with.)