I am a master graduate in the field of material science. I didn't continue my PhD, however, my supervisor involved me as a co-author of a paper (due to my work during my master thesis), and I received so many invitations to be a speaker in conferences all over the world. Can I accept and go abroad to learn from the experience or is there no chance that they will accept me because I'm not a PhD student?
You can of course publish at conferences and journals without a formal degree. There are still some rather famous people in CS who never got a doctorate, though the number gets smaller and smaller, in part because some do get one while they are closing in on retirement. Your MS thesis is not the first one that has been made into a publication.
Be careful however about these invitations to be a speaker. There are many low-level and outright scam conferences and journals, who will not give your work a platform but are solely or mainly after your money. A common strategy of predatory journals and conferences is to go through respectable contributions and send you an email telling you how impressed they are with your work. You need to be careful. One of the disadvantages of not having a terminal degree is the apprenticeship into academia that comes with the Ph.D. Another disadvantage is the lack of colleagues, friends, and advisors that you can ask for feed-back. At least you have your MS advisor, who you can ask before you spend time, money, and effort on fake conferences.
Sure: you don’t need a PhD and you can go there but who will pay?
You should not assume that because you are invited your expenses will be paid or reimbursed. In fact most of the time (but not always) the invitation will get you a discount on registration but you still have to travel to the venue, pay for your hotel and meals.
In my experience, it would be rare for a graduate student (PhD or otherwise) to have lots of invitations for which expenses are paid. It does happen to superstar students, but - in all modesty - conference organizers more are likely to spend their budget on well known researchers with star power who will in turn attract other participants.
Unsolicited invitations to conferences are almost always scams, especially when you receive a lot of them. Ask your supervisor if the invitation looks legitimate, and if so, just be bold and go for it :-)
From first-hand experience, there are usually no requirements for any type of degree. Back in the day, I submitted work from my Bachelor's thesis to a CS conference and got accepted and presented even before I had my B.S. degree. The top 15% of contributions got invited for an extended IEEE publication, and my work was among those selected (I was first author). My advisers were coauthors and did have PhDs of course, but in general all that matters is the quality of your work.
Often, conferences give out travel grants, and as someone who would not be supposed to have any grant money of their own like professors do, your chances of getting support that way might actually be good.
Freeman Dyson never had a PhD. https://en.wikipedia.org/wiki/Freeman_Dyson So it can be done, and one can climb up the ladder quite far.
For average people getting a PhD might be the easier road to such goals though.
It may depend on the conference, but in 2009 I submitted a paper to a well-respected computing science conference, the ACM International Conference on Functional Programming, which passed through peer review, was accepted, and I presented it, despite my having no degree at all (I have only a high-school diploma from a high school of no special distinction). So it's certainly possible.
ICFP is clearly a legitimate (i.e., not predatory) conference and I was not invited to submit. I paid all the normal conference fees that any attendee would pay (ICFP waives fees only for invited speakers) as well as my own travel costs.
Since then I have of course received many "invitations" to predatory conferences, and even invitations to become the editor of predatory journals; this is normal these days whenever you publish a paper. You'll obviously want to avoid participating in those; they exist not to move the field forward but simply to take your money.