As the title says, just one word that describes something with the attribute of having a deadline. For example "Please don’t feel rushed to RSVP as I have no ******". Is there a word that works in this context? I thought about appointment, and that would work, but I'm looking fora word that is a little more general, because a project, for example, has a deadline, but is not an appointment.
The question is too vague and I do not believe you will find any single word which will convey the message you are trying to convey. The closest would be: 'time-sensitive'. e.g. Do not worry about a quick submission for your project as it isn't time-sensitive.
Another case (yours): Please don’t feel rushed to RSVP as I have no time-sensitive registration/seating/deadline/requirement.
If I go by the title of your question "What is something called that has a deadline?" I can think of several: Limited, Transitory, Term.
However, using your example I feel a different word is more suitable:
Please don't feel rushed to RSVP as I have no cutoff.
Part of the problem here is there are at least two ways to take your meaning. Not having a deadline might mean there will never be a deadline. It also might mean the deadline is yet to be established. RSVP seems to imply a singular event but it could be a continuum of events. Consider rephrasing as:
Please don't feel rushed to RSVP as I have no established deadline.
Please don't feel rushed to RSVP as I have no established deadline as of yet.
Please don't feel rushed to RSVP as this is perpetual.
Please don't feel rushed to RSVP as this is recurring.
These last are not exactly what you asked for but sometimes it's nice to have options.
due /d(y)o͞o/ adjective –Google
expected at or planned for at a certain time.
The RSVP is due no less than one week prior.
due date, noun –Google
the date on which something falls due, especially the payment of a bill or the expected birth of a baby.
Please don’t feel rushed to RSVP as I have no due date.