Is it permissible to eat pareve food made on dairy equipment/dishes and pareve food made on meat equipment/dishes in the same meal/on the same plate?
There is a dispute whether one can eat parve food made on dairy equipment with meat (and vice-versa). Sefaradim tend to be lenient, Ashkenazim are strict from the outset (lchathila) and often lenient after the fact (b'dieved). A good summary of those laws can be found here, a simpler one here and the sefaradi view here. Note it is always allowed to eat them one after the other - the question under debate is whether to eat them together.
But here you have parve food on dairy equipment with parve food on meat equipment on the same plate - which is a different case. I can see no reason why this should not be allowed under condition that the pots are clean, not used for 24 hours and that no hot/spicy foods are involved (e.g., onions, garlic, lemons, and pickles). I have now seen that R Yaakov Goldstein answers the same here and checked with R Binyamin Tabadi who concurs with the above.
It is permitted to eat a Nat Bar Nat dairy food with a Nat Bar Nat meat foods although one may not pour the content of either pot directly into each other.
And of course, we are speaking only in theory here. Any application in real life would require consultation with your rabbi as small details can make a big difference.