Well, there certainly are a lot of blood red and ochre and orange walls around in Mexico, so I wouldnât exactly call it unauthentic, but it is a bit too strong for an actual living space IMO. You can find it inside and outside buildings all over the place. My parentsâ previous home had the whole casual living space (TV room) in strong orange. Yuck.
I donât have much of a photography collection from Mexico, but here is one colonial building in Celaya mixing red and orange (actually the building we park inside when we go to downtown Celayaâs market):


That kind of red base plus orange, yellow or salmon upper wall is extremely common.
And here are some traditional, strong colors in San Miguel (used on the inside as well as outside):

And in Guanajuato:

Get a load of this hillside, and all the strong colors, different for each house!

As you can see, just doing the wall base in dark red is very common, or you can do the whole wall (yuck) or just trim (nice). My parents used red tile or brick to do the baseline only, which is far more subtle, and very classy IMO.
Or you can just do a few door and window borders, or columns as here below, in red, with the white and neutral scheme for the remainder, plus black iron highlights â very classy:

Another good color for colonial decor is salmon:

This is my parentsâ house in Mexico:

You can see that the traditional style is alive and well. A large, rustic wooden sculpture makes a nice addition to a patio or yard â you could get one from SE Asia, for instance, and as long as it has a very universal motif it will fit right in.

Oversized pottery as planters works well too.
Some of the above elements can be used to inspire indoor design, without the need to source actual Mexican stuff. If you have interior columns, you can brick them, as I showed earlier, or you can brick partway up, as shown at the top above, top with tile, add decorations halfway up the column, whether black iron lamps as above, or masks, birds, gourds, suns or suns and moons, or whatever, then do a line of terracotta tile along the ceiling above them just like the porch above. You can also use red tile or brick for the whole lower quarter or third of some interior walls, simulating the above-mentioned red painted wall bases, but adding texture.
My folks used the same idea (half-bricked columns) in their central patio, here below, but add a strip of colored tile at the base. Indoors, you could use small colored tiles to replicate that strip in mosaic:

That would be a really fun DIY project, IMO.
They have a line of turtles crossing the patio (we used to have a live one), and Iâve seen turtles like this, but less crudely made, and articulated, in Yingge. Theyâd look nice too. You can also see the kind of tile they use. But any neutral tile will look perfectly fine amidst Mexican decor, as will wood floors.
On walls or floors, you can also intersperse small contrasting tiles. They donât have to be polychrome. Any small geometric or floral will do, like these in Momâs kitchen:


Hereâs the whole kitchen btw:

Now, my folks used a lot of polychrome Talavera tile, like this, in the main hallway:



All the bathrooms use some, either heavily in a more rustic bath, or just with light touches in a more modern bath, as here:



Although Mexican polychrome tiles may be tough for you to get, you could definitely put together your own mosaic, like this one my mom put in:

You can see it in location in the lower part of this pic,

which demonstrates several typical elements: use of a darker colored wall (although here itâs a tame version), arched doorways, and then bright, bold, colorful decoration. This is the entrance to the living room, which has 18th-19th century European-style furniture, and looks just fine, so you donât have to go with rustic if you donât like:

That room wouldnât have looked good with strongly colored walls IMO, but you can do the colored (painted, or tile-covered) walls in transitional areas like halls and stairs and foyers, and it looks cool.
Wall decoration ideas: find small copper, wooden or terracotta jars, bells or similar items, string them together with a rough hemp rope and hang on a wall:


Gourds will work, and you can even paint them, and hang on a scroll bracket like this:

Note also the heavy use of arched forms in many of the above pics. I donât know how far youâre planning on taking the renovation, but if you can incorporate arched tops to doorways, even if just as tile or painted dĂ©cor above the door, that will add some character.