Vietnam has 10 Mio tourists every year now... nothing unsusal any more.

I live in Vietnam and I don't think you would have any trouble to get into Vietnam, but you should check with your officer if there are any policy in the army. I know a guy work in the Air Force and he couldn't travel to Vietnam due to some policy.
And once you travel to Vietnam beware of pickpocket since they often target tourist.

Vitnam 10 : UK 1

Depends on your country.

I can only talk about the German public service, but we can travel to any country we like. Including North Korea and stuff, but that needs to be approved first (by both sides in that case).
I highly doubt Vietnam is on that list. It's fairly harmless.

Speaking as a person who's been to over 100 countries including Vietnam, its more capitalist than eg the USA, everyone there has got their own business. Its extremely cheap, you can live well on $10 a day though you can get by on $3-5 a day (grab some beer hoi on the streets for 20c a glass). The people in the northern half can be verbally aggressive. Unlike the neighboring countries laos,cambodia (though not china) you have to get a visa beforehand, which typically takes 3 days

dont evangelize dude, anywhere

About 8% of the population is Christian and I think Vietnam is pretty loose about religion, so go ahead I would say. Just keep your ID with you just in case.