Would it be appropriate for me to tell people at work my sexual orientation?

Certainly don't do it off the bat (as in just randomly saying "hi I'm gay/pan/other") just for the reason of a) people probably won't care and b) it's a bit odd. But slipping it into conversations fine.

You would need to know how comfortable they are with people of a sexual orientation outside the binary spectrum. It would definitely be appropriate, but it might cause you some problems as people uncomfortable with your orientation might cause you untoward grief.

If you feel comfortable telling people about your sexuality, don’t feel presured into telling everyone, it is ok to take your time with these thoughts

My general thoughts in regards to this is that the only people who have a true need to know regarding your sexual orientation are you and the partners you are looking to connect with. That being said, my next question would be, why has this come up as a question in the first place? Are your coworkers choosing to make political statements about the LGBTQ community under the assumption that they have the freedom to do so? Does your workplace have explicit directives about what conversation topics are appropriate and inappropriate for the workplace? If your coworkers are making poor choices with their words, I would raise a concern with your direct supervisor or HR. There is no need to make an announcement, because it's no one else's business. I guess this is the long answer to say that no, I don't think it's appropriate to discuss sexual orientation at work in general. Unless your work is specifically related to the sex industry or your orientation provides you the opportunity to give unique perspectives that they are seeking for a project or product, there are few circumstances where a coworker would need to know who you found sexually attractive (if you feel these feelings that is). So you need to consider the "why" behind your wondering, and act accordingly.

You should come out whenever you feel is the right time. And also if you are really close with your work mates then you can consider telling people about your sexual orientation because there is nothing wrong in that. If you feel it will make you more comfortable doing that then you should definitely do it. Many think others will judge based on their sexual orientation but you can't hide your true self from yourself for long. You can't live like someone else, if you want you can let the world know who you are and nothing to be ashamed of because it is totally normal.