First, ICANN is the organization overseeing all TLD management at the (IANA) root, so yes you can trust any
RDAP is a newer protocol, intended to replace Whois. It is basically JSON over HTTPS and conveys details about domains (contacts, nameservers, dates, etc.), where Whois was doing the same but in an unformatted unspecified way.
ICANN regulates gTLDs, that is TLDs not associated to countries, which ones are ccTLDs.
com.mx is a public suffix under TLD
mx which stands for Mexico.
ICANN tool for Whois/RDAP queries will mostly work only for gTLDs. Which is what the error message tells you, albeit in an unclear fashion.
Having an RDAP server is mandatory for gTLDs, per ICANN requirements. But not for ccTLDs. Yet, as it is clearly the future, some have one, and hence when that RDAP server exists, the ICANN tool can use it. Try with
nic.uk for example, and it works.
If curious, you can go at https://data.iana.org/rdap/dns.json to see all currently defined RDAP servers along the world, so all gTLD ones (required) and some ccTLD ones.
But you can go at another authoritative source to grab details on this TLD and where to lookup things for it: https://www.iana.org/domains/root/db/mx.html
(IANA is like a service name of ICANN).
You can see that registry website is http://www.registry.mx/ so you can go there to search for details on the name, it is the registry website, the utmost relevant and authoritative source for anything under that TLD and indeed you should go there to do searches, and nowhere else, because everywhere else is just a proxy to that data, which could induce various negative effects.
On above IANA page you can also see:
WHOIS Server: whois.mx
This means you can use command line tools to query for your name, as such:
$ whois -h whois.mx beurer.com.mx
Domain Name: beurer.com.mx
Created On: 2013-01-24
Expiration Date: 2023-01-24
Last Updated On: 2018-01-23
Registrar: NEUBOX Internet SA de CV
Name: Equipos Medicos el Bisturi.com.mx SA de CV
State: Distrito Federal
This is authoritative data coming from registry. There will not be anything anywhere more fresh and correct than that.