I take a solo journey to Mexico every year-
no kids,clear my head trip- and am always
charged a "single supplement"-usually
1 1/2 times the Double one rate- and find
this rather discriminatory. Is there any way around this? Some U.S. hotels do this
also.

How to avoid it?... don't book a package deal. I often travel solo to Mexico. I just buy a plane ticket and book a hotel room myself.

Two ways round it

Make your own arrangements, as suze suggests.

Pick a company that doesn't charge a single supplement, but instead has you share a room with another solo traveler. These are usually small group tours that use local transport. E.g. Intrepid, Imaginative Traveler, Adventures Abroad (mostly).

Another good company that gives you the share option is Cosmos. The risk is that could get a roomie that you can't live with. But if there's no other solo traveler of your gender, you get the single room without paying the supplement.

We'd really need to know that to answer the question... if you are willing to be assigned a roommate and share your room with a stranger.

That's something I'm not willing to do.

I understand the advantages of booking a package when two people are traveling together, because sometimes you can save money. But I've never found a package for going solo, that is cheaper than I can easily arrange on my own.

Isn't Cosmos one of those big bus, it's-Tuesday-so-it-must-be-Paris, pay-extra-for-excursions outfits? Much, much better to do it yourself. And do they even go to Mexico?

I don't know if Cosmos goes to Mexico or not, I was simply adding to the list of companies that allow a single share rate. Cosmos isn't all bad, but I've used some of the companies you named and I do prefer those.

Appreciate the info. I usually use Apple Vacations for the Mexico trip
but will check individual booking.
The supplement has also been charged
at U.S. hotels too.

Could you explain what you mean by a single supplement being charged at US hotels? IME there is a flat rate for the room regardless of how many people are staying in it. Of course, that actually means it's twice as expensive if there's only one of you rather than two (and it's a lot cheaper if there are four), but it's not usually referred to as a single supplement.

I'm curious too (about U.S. hotels). Except for formal organized tour groups, I have never heard of or seen a "single supplement".