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I don't think it's "rude" to not put stamps on your RSVPs. But, like a lot of other PPs have pointed out, nowadays it can be rare someone has stamps. You'll save yourself a lot of time if you just stamp the RSVP envelopes.
I had to actually mail a check to an online pharmacy the other day. I was pissed about it. Because I don't have envelopes. I don't have stamps. I put off ordering MEDICATION I needed by two weeks because it is such a hassle to get to the post office. Especially for someone, like myself, who works a typical weekday job.
With the exception of that recent pharmacy order and not including packages, the last time I sent mail was almost 4 years ago...for my wedding invites, RSVP envelopes, and ty notes.
In addition to what PPs have said, I think you will receive a lot less RSVPs and be forced to make a lot more follow-up phone calls if you don't put stamps on your envelopes. Personally, I don't have stamps at my house. The only time I need them are for mailing things at work, where we have stamps. If there was no stamp on an RSVP envelope, I would probably just call/text, but considering not even everyone RSVPs when IT is convenient for them, I think most of your guests are going to let that RSVP card sit around at their house until they remember to go buy a stamp (which could likely be never).