What type of ear skills do I need: absolute pitch or relative pitch?

Surely if you have good relative pitch and are given a starting note then you'll be fine. I do that when singing solo- and when I finish I'm normally on the right note (give or take a flattened semitone).

It helps to have other musicians playing with you and it helps if you are doing originals. That way it is harder for the audience to know if you drop a few notes here and there to get your bearings back once you get lost.

a great thing about playing with other people is that whenever you mess up you can just shake ur hand and make cool effects and no one notices

With regard to stringed instruments (I play the double bass a little), it's kinda absolute when hitting an initial note, then relative after that, although alot of the time you're not necessarily playing by ear - there are set fingerings on that you learn that get you pretty on the mark.

Some players put a dot marker on the fretboard so that initial notes are found more easily.

Tactile feedback from the strings and board also give you an indication of where you are.

Learning double bass for me was pretty easy, coming from an electric bass and guitar background, because there is a set method that's kinda Lego-like...methinks learning the theremin is gonna be a whole new ball game!

You need relative pitch. Perfict pitch can actualy be a detrament in the real word.

Do you know why oboes are used as a pitch refrence in an orchastra?

Because they are the hardest to get properly in tune. I am gnu to the Theremin (how gnu ... waiting for my kit to arrive today) but I have played bassoon in many orchastras - even to the point of getting paid to do it for a few years - so I know of what I speak.

BTY: Unless groups are playing with an instrament with true fixed pitch - like an organ or piano - they tend towards some version of pure/Ptolemic/Pythagorean intervals.

Also it should be know that pitch can drift with the group. For example most Shaped Note singers in the south tend to sing about 1/2 step flat from the written music.

So to answer your question. I think in the real world try for good relative pitch.

I agree - at the very least, you can have a lot of fun with the theremin with relative pitch & playing along with the others. For soloing, perfect pitch would certainly come in handy, but most of us out there don't have it.