Store hashed email and compare hash values I have a number of different systems sending me email addresses, but I don't actually need the underlying email, just a hash of the email address. I know I can compare hash values to find matches across the senders, which is all I want to do, but what if each sending system uses a different salt or hash method.  Is there some way to compare the resulting hash values I have?

Eg. Sender 1 sends me emails using sha1 and no salt.
Sender 2 sends me email addresses using md5 and a salt (which they also send)

Can I take md5(sha1) and sha1(md5) and compare that hash output? Or do I need to specify that all emails should be hashed using the same method? Is there a better way that will allow each sender to select the hash method they want to use but still allow me to compare email addresses across senders?
With normal cryptographic hash functions, two different ones, or the same hash function with different salts (which in effect are different hash functions too, for each salt) are supposed to be independent of each other, i.e. there should be no way (other than brute-forcing the message) to know from the results if they have the same input.

There are some special constructions of "different" hash functions which do not quite behave that way, but when there are independent salts, you even then have no chance.

As you used the homomorphic-encryption tag on your question, this might be a way to go. For example, with modular exponentiation modulo a prime (or analogously in a elliptic curve group), each sender would have to convert the mail address to a number $x$ (everyone using the same method for this), then calculate $f_i(x) = g_i^x$, where $g_i = g^i$ is a number assigned to each sender (and you know the $i$).

To compare the results $f_i(x)$ and $f_j(y)$, you calculate $f_i(x)^j$ and $f_j(y)^i$. If they match, then we have $(g_i^x)^j = (g_j^y)^i$, i.e. $(g^x)^{i·j} = (g^y)^{i·j}$, which usually means that $x = y$.  (This is a variation of the Diffie-Hellman key exchange.)

The $i$ works as a kind of salt here, so for listeners who don't know $i$, the mail addresses of different systems are not comparable. But I don't see how we could incorporate some kind of sender-chosen random salt for each message.