Cross-training in other Arts and even other styles within Karate was the way of almost ALL of the founding pioneers and inheritors of systems.

Only until post-WW2 did the concept of 'style-loyalty' become prevailent in Karate practice. This manufactured loyalty had more to do with organizational and finacial commitments than so-called keeping lineage 'pure'.

Martial Art lineages are never 'pure'...masters of their Art hardly ever have the opportunity to pass on 100% of their knowledge to one person. often they pass it on over a period of time to multiple people - each person takes away their own 'version' of what they absorbed...and so on. Thats not even mentioning the fact everyone has different influences during their lifetime study. Those influences add and change their 'path'.

anyone trying to sell 'true' or 'direct' lineage is doing just that: SELLING.

let's take a look at some Karate pioneers/founders and inheritors martial resumes PRIOR to them fully developing their system.

Shoshin Nagamine - studied karate when a kid in a neighbors backyard, style unknown. took Kendo in high school. trained another type of Karate with Kotatsu Iha. after H.S. he became a student of Taro Shimabokuro and later Ankichi Arakaki. later, training under Chotoku Kyan, then Choki Motobu. He also corroberated and cross-trained with Chojun Miyagi and his large circle of influences. Initially from Funakoshi's writings, he began to see and add a larger philosophical meaning to Karate...eventually leading him to serious Zen study.

that's seven or eight sensei prior and during his formation and development of his Art that is passed on today.

Sokon Matsumora
Had several instructors, influences and corroberations.
Chinese Kenpo
various Fukien boxing methods
influences from Kusanku via Tode Sakugawa
white crane

and who knows what else or from whom.

Kenryo Higaonna
studied under Sheisho Aragaki
then various art influences and instructors from Fuchou, china
His influences to and from others back on okinawa were too extensive to list. The Art he taugght was VERY eclectic.

In fact, it might be easier trying to find ONE significant Karateka which did NOT have multiple influences and teachers.

There is a rich heritage of sharing Arts in Karate ...not necessarily to the public, but within trusted and advanced circles regardless of 'style' (which didn't have as much meaning then since everyone was a bit of this and that).

All karate under it's surface is the same, the variations are in the way that base knowledge is prioritized and expressed.

The ONLY reason instructors now address cross-training in the pejurative saying things like:
"student of many, master of none."
"dojo hoppers."
"watered down."
"impure lineage."

etc...the only reason why it is just now frowned upon is because either:
1. They have bought into it from their sensei telling them the same.
2. They have a business/reputation to protect their 'product'. They see their Art as a trademark not the mark of a trade.
3. Student retention. If an instructor's Art can stand on it's own, they need not fear their students to be aware of what else is out there. an instructor telling students: "you need full comitment to THIS art...or you'll get nowhere in your path" -is frankly, full of doo-doo.

next time they say that, ask them what influences their style founder had...and why the style-loyalty rule didn't apply to them for gaining proficiency in Karate.

I once asked my current instructor: "Do you mind when I meet and train with others and of dissimilar arts?" he said: "Heck no...if you see something good, share it and we'll take a closer look at it."

I think thats the way it once was.