I am only recently finding this out because it is happening to me now as well. In the past it has happened to many other expats living in Vietnam but I guess I was given a sort of grace period because of my special visa status. I'll touch base on that in a bit because it in itself is kind of a long story.
Basically I'll put the tl;dr right here at the start.
If you do not have a work permit the banks often will not let you have an account at all and even if they do they will not let you have a credit card or even something resembling something like a credit card.
This has only come into being in the past month as this is when my Vietnam bank-issued Visa stopped working.
There are a lot of different banks in Vietnam and up until recently there was some question about whether or not a foreigner would be allowed to have an account there. When I First got here in 2020 whether or not you could get an account seemed to be almost completely based on how the bank staff were feeling that day and if you were friendly enough. Some people got them, other people didn't and those that were refused were often given BS reasons for why they were not allowed an account only to try at a different branch and be given an account.
it still remains a bit up in the air right now about why someone isn't allowed an account without a work permit and also whether or not the individual banks are actually going to do it or not. From my friends, some of whom are Russian, American, and also Norwegian, they were flat out told they cannot get a bank account and they simply ended up opening an account in a Vietnamese person's name and treat the account as their own.
Honestly, if you have a Vietnamese person that you trust enough, this is definitely the easiest way to go because they will never be questioned but of course should you ever have a problem one day or someone asks you to prove that the account is yours via ID of some sort, you will not be able to do so. It does help for people just trying to make online payments though.
When I initially got my bank account here in Vietnam, I was issued a Napas card. I do not know what Napas is but I am presuming it is something that is local, Vietnamese, or at best, just an Asian thing. So when I was going to be traveling to North America i went to get an international card and they issued me a visa. Neither of these are credit cards, they are both debit cards and will only allow me to spend as much money as I have in the account. We all know what that means.
About a week ago I was trying to purchase something on Lazada, which is our version of Amazon, and it has my visa card stored on it, and none of the purchases were approved. There is another app that I use for taxis and food delivery that when I set it up, I only had my Napas card. It still functions but I discovered when I was visiting Thailand, it would NOT work when I was there. This is the limitation of the Napas card I guess.
I haven't been in there to question the staff about my visa card yet, but as it stands now the card doesn't work at all on line or in person. It does still work at an ATM. So this entire process is rather annoying and according to my agent there is nothing that can be done to change this.
I do not know why the government has decided that you as a foreigner are not allowed to have a debit card to access your own money but that does seem to be the case.
Basically, if you are a non-Vietnamese person living in Vietnam and you do NOT have a work-permit, and this is going to be anyone who doesn't work here, then you cannot have a card that is going to be at all useful during international travel.
This is rather annoying and I don't know the justification for it but people should understand that while the Vietnamese government does a good job of letting you live your life over here without bothering you too much, they also NEVER give an explanation for why something has changed. It just changes and you have to accept it. I suppose this is that communism that I have been hearing so much about but never really experienced.
There are other methods of getting money in an out of Vietnam but if you want a local account, it seems as though that this is not an option for non residents anymore. boo hoo.
Maybe this will change in the future. If you are just visiting here nothing has really changed. ATM fees are very low here and your international card will function normally.