Unfortunately, I do not have time to do a thorough analysis, but I am fairly sure that you are a former Dutch national, and this is why:
When you were born, you were Dutch because your father was Dutch (assuming your parents were married) or because your mother was Dutch (if your parents were not married).
When your parents naturalized in 1969, you did not lose your Dutch nationality. (You would have lost Dutch nationality if you had acquired US nationality as a consequence of your parents' naturalization, but because you were already a US citizen, that did not happen. I believe my uncle, born in 1938, retained his Dutch nationality for this reason when my grandfather naturalized in the mid 1950s.)
However, a new Dutch nationality law went into effect in 1985, on January 1st I believe. That law provided that a dual national who was born in the country of other nationality (for example, you), who lives for ten years in that country after reaching the age of majority, loses Dutch nationality. The ten-year period starts on 1 January 1985 or on the 18th birthday, whichever comes later. In your case, it started on your 18th birthday, which occurred during 1985. Therefore, you lost your Dutch nationality on your 28th birthday in 1995.
However, if you lived outside the US between 18 and 28, you may have delayed the loss of Dutch nationality. (The current rule discounts periods of absence of less than 1 year, but it might have been different then.)
There is at least one other exception that has applied to certain versions of the 10-year rule, though I do not know if it applied to this version. The exception is being married to someone who is posted abroad in the service of the Dutch government. In the current version of that rule, the spouse may also be serving an international organization to which the Netherlands belongs, so if you were married to someone working at (for example) the UN or the World Bank, you will want to check whether that was the case in the 1985 version of the rule. There may have been other exceptions; I do not remember off the top of my head.
The mechanics of the 10-year rule were subsequently changed, so if you lived abroad for long enough (or were married to a Dutch consular employee or similar) then you may have a chance. But without knowing more about your circumstances, I can only say it is a very slim chance indeed.
To answer your other question: If you do in fact manage to establish that you are a Dutch citizen, you may indeed retain both your US and Dutch citizenship.
As a former Dutch citizen, you may be interested to know that there is a simplified and accelerated naturalization procedure for oud-Nederlanders, but it does require first getting a residence permit and (if I recall correctly) living there for at least a year. It would also require you to relinquish your US citizenship unless you qualify for one of the exceptions (such as being married to a US citizen, if I recall correctly).
I just found an article that I haven't had time to read, but it looks fairly good. It has a lot of detail on the subsequent changes to the 1985 10-year rule.
The government has a lot of information on this because it is so complicated. The public-facing information pages (in Dutch from both the main government site the IND, and in English from the IND) do indeed gloss over some of the exceptions, so don't take them as gospel, but they should give a pretty good idea of the current state of the law (for example, of the naturalization procedure).
And oh, just as I was looking for the link to the government's pages, I found this, not yet two months old: Beoordeling gevolgen verlies Nederlandse nationaliteit:
15 juni 2020
Oud-Nederlanders die sinds 1993 het Nederlanderschap en het burgerschap van de EU hebben verloren, kunnen die mogelijk weer terugkrijgen. Een online tool helpt deze groep Nederlanders om te bepalen of zij inderdaad hun Nederlanderschap zijn kwijtgeraakt. In dat geval kunnen zij een zogenaamde evenredigheidstoets aanvragen.
June 15, 2020
Former Dutch nationals who have lost, since 1993, their Dutch nationality and EU-citizenship since 1993 may be able to get it back. An online tool helps this group to determine if they have indeed lost their Dutch nationality. In that case they can request a so-called proportionality test.
It goes on to imply that the test considers the personal consequences on you of having lost EU citizenship, so in your case this also may be of little help, since you've been living all your life without the benefits of EU citizenship. But it's also worth checking out a little more thoroughly than I have time for at the moment. Even a past tourist trip to the EU would be a case in which you could have used EU-citizen rights but were not able to.