I recently talked with a professor about his offer to me a postdoc position. Later on I was notified about an interview for a tenure-track faculty position. So, I am wondering, if I have accepted the Postdoc offers, can I still proceed with the faculty position interview? I don't want to lose the postdoc offer, and also the opportunity of the faculty position. How should I deal with the situation without causing any ethic issues?
If you haven't yet accepted an offer you can search and evaluate other offers freely. If you get an offer but haven't accepted it, that doesn't change. But ethically you should cease efforts after you accept an offer unless you also ask the PI to let you explore something that might be better. That puts you at risk of having the offer withdrawn, of course and bad feelings all around. And accepting an offer may be legally binding in some cases, depending on various things.
But until you accept an offer, even if it is offered, you are still free to explore all options. It is actually wise to do so.
In the current situation, if I understand it correctly, the professor may not be able to make you an offer adequate to your needs. In such a case it is more important that you keep your options open.
My understanding of the norms in academia is that tenure-track and tenured positions are generally accepted to be rare opportunities, and that taking those if offered is the right thing to do. As such, it is perfectly acceptable to attend an interview for a tenure-track position, and to accept it if offered, even if one has already accepted a conflicting postdoc. In such case one should, however, be apologetic to the snubbed postdoc mentor, and do ones best to minimize the inconvenience to them.
I have a suggestion that might win you the best of both worlds. Why not accept the postdoc position for a fixed term, say for 6 months or 1 year as convenient to all parties. Then, in case the tenure track position works out, you can always give (or negotiate) a join date for right after you finish your postdoc position. The additional experience of a postdoc just before you start a faculty position can be invaluable for getting a smoother transition from being a graduate student to being a professor.
My 2 cents (alas no guarantee for success because it depends on the externals as well).
It depends a bit on the professor, but they are academics and they know the game. I would be frank and open to them. Everybody knows a ternure-track is a superb opportunity for someone at postdoctoral level.
I think the main thing here is to see what the time scales are (and I think it is ok to ask the other group what their expectations on the duration of the process are).
If it's short, you may arrange with the postdoc-prof that you take some time to think about the acceptance, or you could ask the other group to delay the hiring a bit. It's a long-term position anyway so funding running out is probably not an issue. Also, they probably have to take into account that people move in from far away, needing them to organise stuff which takes time. This meanse there could be some time in their process that you could use to get a decent postdoc job done.
If it's going to take half a year to a year, you can just start the postdoc and happily continue the application process.
Yes, this could get the offer withdrawn but starting a search is quite some work as well so if you and the professor have a cooperative attitude finding a solutions should be doable.