It's not the oxalic acid, it's the calcium:
Potassium oxalate did not influence iron absorption in humans from a kale meal and our findings strongly suggest that OA in fruits and vegetables is of minor relevance in iron nutrition.
In short, calcium is extremely digestible in chloridric acid (some people even use it to polish marble)...
No, iron supplementation is not necessary for all vegans.
Furthermore, iron supplementation can be dangerous if it isn't a medical requirement. Any person considering adding iron supplements to their diet should have a conversation with their doctor or a registered dietitian to assess their individual needs and the safety of a particular supplement.
Tea and coffee are well known as inhibitors of iron absorption, because both contain caffeine, polyphenols and phytates. Morck et al (1983) studied the effect of coffee on iron absorption in healthy humans. The main findings were:
The inhibitory effect increases with concentration. A cup of coffee ingested with a meal resulted in a reduction in absorption ...
According to The Vegan Society's iron leaflet
relying on non-heme sources of iron gives the human body control over absorption sufficiency, by allowing it to increase uptake to suit its needs.
So this should not be seen as a problem.
Oxalic acid is broken down by cooking, and, besides being a source of iron
Spinach has a lot to offer nutritionally: ...
Consume equal parts spinach and orange/lemon juice for best absorption of iron. It’s okay to drink more orange or lemon juice than that, but it might be more costly.
The presence of vitamin C is most important when eating foods that also contain inhibitors of iron absorption. Orange juice and spinach are a great combination.
The promotion of iron ...
A 2004 study of 75 vegan women in Germany showed that iron deficiency was substantially more common among vegan young women (40%) than the baseline for adolescent girls and women (11%) in the United States. However, only 4% (n=3) had iron deficiency anemia which is about the same as baseline.
A 2015 study of 60 young women in India (30 vegetarians) showed ...
I have been a vegetarian for over 50 years and a vegan for much of that time and have never taken any supplements of any kind. So, in my case, I can safely say the answer is "No!" However the plural of anecdote is not data and things may be different for you.
While a person on a mixed (animal/plant) diet, even the one who has really bad eating habits (unregular meals, a lot of junk food), rarely needs to worry how to get enough iron, vegans should counsciosly think to consume enough iron-rich foods. However, iron supplements are needed only in case of proven deficiency.
Plant foods high in iron (USDA.gov):