Try using an automation for this.  Set it up so that it triggers whenever any of the relevant fields in Source One are updated, and make it:
1. Find the record in Master with the same email
2. Update that record with the relevant data

And you'd create the same automation but for Source Two

Thanks. I haven't looked at automation but will do so.

Can you not build relationships in Airtable like you can in other database programs?

Hi,
Inter-base connections established via sync.
Connections between tables inside the base - with links.
Their functions are different.
It seems like functionality you described is exactly what 2-way sync doing with "Allow to edit record in source" enabled, but I'm not sure.
Are you talking about 2 different sets of the same-formatted data?
Like 40 records in Source 1  and 60 records in Source 2 and summary of 100 records in Master?
Or you mean all same 100 records in Source 1, 2 and Master? And if you edit something in Source 1,  same change happens in Master and then synced to Source 2?
The first is usual multi-source sync, second is 2-way Sync , new feature with some limitations.

to be honest, I don't understand how automation triggered in Source should find a record in Master if it's 2 different databases. 

Yeap, you'd do that via linked fields: https://support.airtable.com/docs/linking-records-in-airtable

You want the data from "f_name" and "first_name" merged into a single field though, and so using an automation to update the fields seems like the easiest approach (to me anyway!).  If you wanted to use linked fields for this you'd:
1. Create linked fields in Master to Source One and Source Two
2. Create last modified time fields in Source and and Source Two for the "f_name" and "first_name" fields
3. Create lookup fields in Master that display "f_name" and "first_name"
4. Create lookup fields in Master that display the lookup fields from Step 2
5. Create a formula field that will see which lookup field has the latest time, and from there decide whether to use the value from "f_name" or "first_name"

And you'd need to repeat this process for every field you want to display in Master which seems quite tedious

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@Alexey_Gusev 

re: to be honest, I don't understand how automation triggered in Source should find a record in Master if it's 2 different databases. 

Ah, I was assuming Source One and Source Two were tables that were synced into Master.  You're right, that's not mentioned in the original post, sorry!

Alexey_Gusev.

Perhaps an example will help. Currently, with desktop relational database software, I have something like this.

Table 1 = Master list with 30,000 records. Unique field is email

Table 2 or Table 3 = A new database that I bring in. The ONLY thing I know about these databases is that they ALSO have a unique email field. And they also have most of the same fields (f name, l name, company, address, etc)

So, I create a relationship (connection) between Table 1 and Table 2 using the key field of "email" in both. I map similar fields from Table 1 to Table 2 (e.g., f name > first name, l name > last name, company > co, etc.) And I set up the relationship so that if there are matching records (same key exists in both) between Table 1 and Table 2 the following happens:

Any records that exist in Table 2 but not in Table 1 are added to Table 1
If a record exists in both tables, Table 2 will overwrite the data in Table 1.

Basic relational database stuff.

Other than creating a relationship based on unique key in both tables, and mapping the fields, I don't need to do anything else. The updating of Table 1 based on Table 2 is purely due to matching keys (emails). If I reimport new data into Table 2, Table 1 will be automatically updated. Ditto process for Table 3 and Table 1.

Make sense?