How can a reentry permit impact my ability to apply for U.S. citizenship?

The re-entry permit per se will not be a problem when applying for U.S. citizenship, but you will still need to be physically in the U.S. for half of the time in your last five years. If you decide to apply the earliest time you can, you are correct. That would be five years after you obtain your conditional green card, but in addition to physically having to be in the U.S. for at least 2.5 years, you will need to be "not absent" from the U.S. for more than six months at a time.

To be eligible to be a citizen you must be a PR for five years with at least half of the time physically present in the U.S. and no breaks greater than 180 days. A re-entry permit allows you not to abandon your PR but delays your citizenship eligibility in most cases.

The five years of residency is physical residency in the U.S. The re-entry permit stops the time counted towardsthe residency to apply for your naturalization. Furthermire, only few days ago, the definition of residency changed to mean that you have to be resident of the U.S. Visiting the U.S. on a short-time basis or even owning a house and filing taxes does not count towards residency if you do not actually reside in the U.S.!

The re-entry permit, which may be as much as two years, will allow you to count the period you spend overseas toward the residency requirement for naturalization.

The re-entry permit, if approved, will help you re-enter after an extended absence. Regarding citizenship you have to be physically present for 50% of the time and not be absent for more than six months, or the continuity of your absence can be questioned.

The U.S re-entry permit will help you only preserve your lawful permanent resident status. You must still reside half of the time physically in the U.S. for five years from date of your conditional lawful permanent residency and never be out of U.S. for six continuous months or longer. Otherwise, you will be deemed to have interrupted your residency for naturalization purposes.

The five years does continue to run while you are outside the U.S. with your permit. But to apply for citizenship you will have to have been in the U.S. for half the time out of the last five years (2.5 years present inside the USA).

It may impact the physical presence requirement for citizenship.