TL;DR: if your flower is in the US or Baja, it's C. menziesii. Otherwise it's C. ciliata sensu stricto.

While we should institute this change because Calflora supports it, they are following Jepson's treatment as described at http://ucjeps.berkeley.edu/eflora/eflora_display.php?tid=95066

According to Hershkovitz (2006), Calandrinia menziesii [Calandrinia ciliata var. menziesii (Hook.) J.F. Macbr.] is available for plants that have been called Calandrinia ciliata (Ruiz & Pav.) DC. in western North America, which are phylogenetically distinct (although not very morphologically distinct) from plants going by this name in Central and South America, where the type for the name was collected. In fact, Calandrinia menziesii is most closely related to Calandrinia breweri, whereas Calandrinia ciliata is most closely related to a species in South America.

Hershkovitz (2006) is available online. Here's the key passage that tells us what to do with observations from North America including Mexico:

Calandrinia menziesii, which is distributed from Baja California to British Columbia, historically has been considered as a variety of the Central American and South American Calandrinia ciliata (e.g., Macbride 1931; Munz & Keck 1968) or even as the same species (e.g., Kelley 1993). Calandrinia menziesii also has been considered as a variety or as the same species as Calandrinia caulescens Kunth (e.g., Gray 1887), but the latter is generally considered a taxonomic synonym of Calandrinia ciliata. In any case, there has never been a clear morphological distinction between the temperate North American versus the Central American and South American plants. The characteristics of Calandrinia menziesii mentioned by Macbride (1931), "more numerous stamens (often) and larger flower," are actually highly polymorphic in this species. In fact, the taxonomic recognition of Calandrinia menziesii appears to have been among North American populations rather than between these and those of Central America and South America (e.g., Gray 1887; Rydberg 1928). Both the ITS and ycf3-trnS data show that the Calandrinia menziesii samples (spanning Baja California to British Columbia) are divergent from those of Calandrinia ciliata (Mexico and Argentina).

So, all North American C. ciliata from Baja up the Pacific Coast should now be called C. menziesii. Plants from the rest of Mexico down through South America should be called C. ciliata. Also, if you're an American and you don't like the name "Curnow's curse," I suggest you go to http://www.inaturalist.org/users/edit and set your place to "United States" or somewhere in the US, because I've made "red maids" the default common name for C. menziesii within the US.