TL;DR : You have every right to use them, but you might get unpleasant comments about it.

Long version :

The spelling recommendations of 1990 have always been criticized and frowned upon in France.

Part of it is due to the media and their oversimplification : a lot of people still think that these recommendations are supposed to replace the traditional spellings, and that they recommend to write éléfant instead of éléphant !

There’s also some kind of a conservative spirit concerning the French language : there are people who think that our language should not evolve and that it should stay the way it was centuries ago « when people knew how to write properly ».

In fact, most people don’t even notice that they are using new spellings everyday : the word « événement » (traditional spelling) is often written « évènement » and no one even bats an eye !

Still, these recommendations have been introduced in the major French dictionaries and should be accepted as correct, and most of the comments you’ll get from using these spellings will come from people unaware of their existence.

P.S : A very interesting article from the Académie Française was published two years ago after an umpteenth controversy about it :
http://www.academie-francaise.fr/actualites/lacademie-francaise-et-la-reforme-de-lorthographe

As you didn’t deny my guess, I assume the edited question you are referring to was this one so I’m the person who edited out one (not several) instances of reformed spelling.

If that is the case, you are right in stating that I should have left that word unchanged.

There was however in your question a significant number of mistakes much more serious than the missing or not missing circumflex, so I would recommend that you not worry too much about the 1990 reform.

Native people will quickly spot gender issues, like phonèmes moins communes, typos like heurs vs heures, locateur vs locuteur, ungrammatical constructions like en l’Amérique du Nord est, supposons que celles soient les seules phonèmes de français, écrites en l’Alphabet Phonétique International, la différence entre certaines d’elles disparait.

I did a significant rewriting of your question and indeed used the traditional spelling disparaît without even paying attention to the fact that yours wasn’t incorrect.

As an analogy, let’s say someone writes this sentence in a question:

It is of the colour of the car of my brother

Someone might improve it to something like:

It has the color of my brother’s car

without noticing that color replaced colour, not because it was a mistake but simply because it’s the way (s)he writes and the focus was on the idiomatic way of saying it.

Answering your questions:

Should I use the spelling reforms of 1990?

It’s up to you. You are free to use all of the reformed spellings, some of them, or none. Just try to be consistent and not mix traditional and reformed spellings of the same word. If you choose to fully support the reform now, note that you’ll be part of the early adopters group so you might be considered somewhat nonconformist.

Has the French world accepted these spellings?

Some people will never accept the reform, just like what already occurred with all of the previous reforms that recommended new rules. This isn’t a (long-term) problem – people eventually die while reforms have a better resiliency. The vast majority of people will stay unaware of the reform’s details and just keep writing the way they’re used to, which means some of the reformed spelling will be used, some traditional spelling will be used, and some bogus spelling will be used too…

Nowadays, more and more people also rely on assisted spelling correction tools so when the reformed spelling start to be the default one (assuming it ever does), adoption might be boosted. What is taught at school will also shape the fate of this reform in the long term.