Finding a place to stay in Cancun (or anywhere really) as a single male

This is an interesting question, thanks for asking it, and congratulations on deciding to travel. Personally, I find travel very rewarding.

I am not sure if you are looking for a hotel, guest house, or resort, and possibly you have not decided yet. When reading through reviews, see if any mention kids or drunk younger people. I've read countless reviews of hotels I am considering where people mention how accommodating the hotel was to their kids, etc., so that can be a hint that other people will bring children. I've also read reviews of places, for example beach hotels and guest houses in Phuket, that complain about too many drunk young Australian guys, so that is a clue that the area is one where being somewhat drunk is expected.

I don't know if you want a place where you can be left alone, or one where you are likely to meet people. There are many places where one or the other is more likely. Most large hotels cater to single people, and you will be left alone if you want that, or can hang out in the hotel bar and have a better chance of meeting someone. There are resorts with communal dining where you will have a good chance of making friends. At more isolated resorts (further from a town) you will likely see the same people all the time, which may make it easier to make friends or join people for group activities, if you want that.

If you are looking for intimacy, there are singles resorts where other single people will be. If you are gay, bisexual, or unsure, there are hotels, resorts, and guest houses that will be especially friendly and welcoming.

Wherever you decide to go and stay, I am confident you will enjoy it.

I have not traveled much in North America and most of that was in company, my travel experience is mostly in Europe, with a few good trips beyond.
Traveling alone outside Europe I have done 6 weeks in Australia, 6 weeks in New Zealand, 4 weeks in Japan, 4 weeks in Canada.
In most cases I have used hostels and 'bed and breakfast' places, in more recent years single rooms in hostels rather than dorms.

And that is what I suggest to you. Look for a city or (national) park area, and see if there is housing for people moving around. Book a single room in a place that does dorms or book a room in a house where there are only a few rooms. Hostels have the added bonus that people usually spend some time in a common room, making meals, having breakfast, so you can make contact but at the same time you can retreat into your own room when you feel that need.

An other thing that makes traveling alone good is joining day tours or even multi day tours as long as you can book a single room on those tours.

Start out with short holidays, maybe no longer than a long weekend, and build up once you are happy with those.

If you have noticed that I do not give attention to your age, gender or anxiety tendency, you are right. I do not think they matter or said the other way around, maybe other people will do other things, but I think you and I are both going to be happy with what I usually do.

With the exception of some resorts that explicitly cater to couples, and some that explicitly cater to families, almost all resorts are going to accept singles. The couples and family resorts usually say what they are very clearly up front, so you can avoid them.

The usual issue is that as a person travelling alone at a resort you have to pay a single supplement. Look for "double occupancy" written somewhere near the price. That tells you that with fewer than 2 people in a room, you will need to pay more than the quoted price. The supplement is often difficult to find, and may be impossible on consolidation site - you may need to go to the website of the resort itself. If you are just booking a room, then the room price stays the same even if there is only one person in it.

The atmosphere of the resort, in terms of single-friendliness, is more difficult to determine. Be aware that 'single-friendly' may mean it's a place for partying, drunkenness and hookups. Since you describe yourself as having 'social anxiety' that may not be what you are looking for (or it may be exactly what you are looking for). You will have to do some reading between the lines to determine what kind of resort it is. Look at the resort description and any pictures the resort publishes, to see if they are of couples or families, or of large groups of people. That tells you how the resort is advertizing itself. Look to see if there is a kids programme. Is there a club on site, or advertized as nearby?