Who can participate in international conferences in mathematics? Does one have to be a mathematician or affiliated as a researcher in a university to participate? How about Independent researchers (with an undergrad diploma)?
Pay the registration fee and go. Conferences are generally open to all paying customers. In order to give a talk, you will have to submit a paper, extended abstract, or abstract based on the instructions in the call for papers (or participation) and have it reviewed and accepted. But neither kind of participation requires a credential, typically.
It all depends on what you mean by a "conference". If you are talking about a large organized meeting open to anyone in the field, then I agree with Bill Barth's answer: there are no formal requirements at all for attendance, and anyone can simply register and show up. If you submit a proposal for a talk or poster, then it might be rejected, but the rejection would be because of skepticism about its value or fit for the conference rather than just because of your lack of credentials.
There are also lots of smaller workshops, for example at mathematics institutes such as MSRI or Oberwolfach. These workshops are more likely to have limited attendance, sometimes by invitation only and sometimes with an application process. There's no rule prohibiting non-academic attendees without graduate degrees, but getting accepted under those circumstances would be remarkable. There are generally more applicants than places available, so the only way to attend would be to convince the organizers that replacing a professional mathematician with you would be an improvement. That could happen if you have a sufficiently impressive track record in the field, but it's not likely.
The answer depends on what you mean with "participate". Attend, or give a talk?
Who can participate in international conferences in mathematics?
Attendance: anyone who is registered, possibly with conference fees, although a lot of mathematic(s) conferences are cheaper than in other fields. Warning though: there is an increasing number of scam/spam conferences, that accept any audience, and your international math conference will increase your knowledge by the empty set. I cannot give names (been threatened by lawyers for these crooks), you have to find out by yourself that the conference has quality.
Talk: anyone who is accepted or invited. If your work is of quality, and the submission format is not suitable, being invited or backed by a known/active mathematician might help. Doxa says that in mathematics, quality prevails over reputation more that in other fields.
Does one have to be a mathematician or affiliated as a researcher in a university to participate?
Attendance: no, maths are universal. They can be used (and are) in every other fields, and shall not repel non-math people.
Talk: it may helps, of course. "Only the rich get credit" is partly valid everywhere. Possibly less in maths. I have attended a conference on scientific evaluation (scientometrics) and bibliometry in 2007 in the French Academy of Science. Non-mathematicians talked about impact factor, reputation, number of papers, number of citations, place in the author's list. A mathematician only said:
"I care about quality, so I read the paper and see if it is good. If I do not understand it, I handle it to a colleague who can understand so that s/he tells me it is good"
How about Independent researchers (with an undergrad diploma)?
Mathematics is filled with non-professional, independent stories. Remember Joseph Fourier was a prefect/governor by trade. Recently, Yitang Zhang made the news around finding finite bounds on gaps between prime numbers. He is described as "a mathematician virtually unknown to the experts in his field", "working for several years as an accountant and even in a Subway sandwich shop", in Unknown Mathematician Proves Elusive Property of Prime Numbers. Which does not mean this is piece of cake, since the field has its rules and codes. If you write a novel proof, and want it to be recognized, you are advised to do your best to make it accepted.