Bottom line
If you plan to leave the United States, the rules depend on how long you will be gone. For trips of 60 days or less, you submit a written notification at least 60 days before you depart. For travel or residency over 60 days that stops you from participating in the SELRES, you request a transfer to the IRR. There are also rules for training while you live overseas, how you travel for that training, and what uniform to wear during official travel.
What it means for you
Foreign travel is not banned. It is managed. The single number that drives everything is 60 days. Under 60 days is a notification. Over 60 days, if you cannot participate, is a transfer request to the IRR. There is a separate carve-out: if you fly for a U.S. commercial airline, short trips (under 21 days) do not require you to notify your command. If you are in the IRR or IMA program, your point of contact is the Director, Marine Corps Individual Reserve Support Activity (Dir MCIRSA), not your unit chain. And if you ever get transferred to the IRR for this, you must resume SELRES participation within 60 days of returning to the continental United States (CONUS) or you can be administratively separated.