Once you join Equity, you may not act without an Equity contract or permission from Equity. Sometimes Equity will give you the ok to do a non-Equity project, especially if you live far from Equity theatres. Sometime a non-Equity theatre can use a guest Equity contract. People who do not follow procedure can get into a lot of trouble.
The person who is auditioning for SETC--if an Equity theatre wants you at that audition, go for it. It's really not as "political" and maddening as it probably seems to some of you right now.
The advise is this--don't join Equity until you are ready. And auditioning is easier in NYC if you are Equity--but you don't have to be Equity to get an Equity job. If they want to hire you, they will make you Equity. And in most cases (though not all has we all have seen bad performances) if you are good enought to get hired in the part, you are good enough to be Equity. It's a personal decision.
But I don't see it as being such a dilemna. If you want to act on Broadway, you have to be Equity. If that's your goal, then work towards it. If not, then stay non-Equity.
If you want to do film, you have to join SAG. If that's your goal, work towards it.
But these are non-profits unions that, good or bad, are there to protect an actor and/or stage manager's rights and wages, etc. And if it's not your thing, then don't do it.
There have been many brutal fights on here about the subject that I just have no desire to go through again. For me, I want to work on Broadway, Off-Broadway, National Tours, and leading roles in regional theatre. So, the choice to work towards becoming an Equity actor was simple. It was always a given.
And after years of working in non-Equity theatres, I got tired of the low or no wages and even more tired of the shotty working conditions and scheduling problems. I went to school and have spent many years working on my craft. I felt (and every performer should) that I deserved to be treated better and compensated for my work. I should be able to make a living as an actor when I have the chance to do a show. For some people, it's a hobby--and there is nothing wrong with that.
So, you just have to make those decisions for yourself. What do you want? And how do you get there?