I'll try tackling this based on my own experiences in my own workplace. I have had a pretty strict christian upbringing (read: completely homo-phobic). I have been attended to this fact by co-workers before, that initially my reactions upon learning that a co-worker is LGTB are not really appropriate. I am trying to improve this, but my initial reaction is still somewhat cold and distant, clearly showing some disagreement and trying to move to a different topic as soon as possible.
First of all, this is highly dependent on your workplace. If your co-workers are discussing their weekends at the coffee machine on Monday morning, or Friday afternoons while having a drink, you are certainly right in wanting to disclose this information to avoid awkward situations. If private matters are never discussed in your workplace, I would keep my own matters private as well.
You can not, and will not ever be able to control peoples reactions. I can say that if you disclosed information as described in your question to me, my first reaction might be experienced by you as hurtful. You can also never avoid discomfort, and should be prepared to encounter a period of uncomfortable encounters after disclosing your information to co-workers.
I would advise you to use some peer pressure. So don't pick the most friendly people first, as suggested by @apaul34208, but all of your co-workers at once (or make sure there are accepting/friendly persons present when you disclose to people that you think might not be as accepting). The good people will probably act as an example, and might even be helpful in backing you up if reactions from the bad people run completely out of hand. For me, the presence of others gives me the opportunity to remind myself that what I was taught for about 20 years of my life is not the right way to react, and to prepare a more proper reaction.
Don't be offended when people let you know that they do not agree with your lifestyle. Let them know that they have a right to disagree, but explain to them that you wanted this info in the open before some stumbled upon it, since you know this in controversial info, you have had people stumble upon it before and thus land you in situations where you could not remedy their discomfort. Tell them (because some might not realize it themselves) that you are absolutely not different from the person they knew before the information was disclosed to them, and that for your part, this also counts for your work-relationship with your coworkers. The drag queen thing is something you do in the weekends, just as advocating LGBT rights is something you do in your spare time, and keep separated from work in all cases, except for this case of disclosing that you do those things, to avoid even more uncomfortable situations.
Please be prepared to 'agree to disagree' if you disclose this information, and leave it at that. If your co-workers are not treating you differently after disclosing the information, but are not enthusiastic about it either, do not start conversations about it. It should not be necessary, but do not try to force conversations about it with people that have not shown to be interested. In short: don't talk about it unless spoken to. Just keep the contact with these co-workers purely business (Could you pass me the stapler?), and hope they will thaw out when they realise that you are prepared to not force discussions about it with them. For some people it can take a few months to process the information and realise that it really is not going to kill them working with you.
If your coworkers keep sending hurtful reactions your way after the first discussion, say to them that their reactions are hurtful. You are not trying to 'convert' them to be drag queens, so they should not be trying to 'convert' you. But you get to be what you are, just as they are what they are, especially since you are only a drag queen in your spare time. If they keep insisting on having hurtful discussions with you, go to HR/whatever party is responsible for workplace diversity and complain. Make sure to let the co-worker(s) in question know that their behaviour in the workplace is unacceptable.
If relations between you and your co-workers show no sign of slowly returning to 'normal' (as they were before disclosing the information), then I think you should not want to be working with these people (easy for me to say, I know). But in the end, you and your co-workers should all be grown-ups and perfectly capable of at least maintaining a business relationship.
What is a drag queen? Is it just a weird hobby? Why do you do it? What do you like about it? Does that mean your gay? Can I come and see a show? Will that be safe for me? Pretty uncomfortable situation if someone blurts out this questions to you... But, these are some of the questions I could blurt out when you told me this. Yes, I had to actually google what a drag queen is (saw some awesome make-up and dresses btw). Answering questions, how stupid they might seem, with a lot of patience, can greatly help furthering understanding and thus removing discomfort. And be prepared to be tackled on your way to the coffee machine three months later with another list of even stupider questions because I have been thinking and ...
TLDR: You can not control initial reactions, but by choosing your moment and preparing a little 'defensive' speech (sadly necessary), and providing your co-workers with options like 'I will never mention it again', you can hopefully achieve a lot.