I am in the same situation, but am not too concerned.

I don't put my social security account number on the card, nor any banking information. I don't think much of the information on it is particularly useful to a thief. The credit cards and money is more useful to them. Medical conditions, drugs, who to call and medical insurance info only on the card; hard for them to turn that info into cash, I think.

And, I almost hate to say it, but the risk to my health and life of being without that information being available is worse than any potential financial loss or identity theft.

Note, I also wear a med-alert pendant engraved with the most critical med info.
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"Better is the enemy of good enough."