Would index lookup be noticeably faster with char vs varchar when all values are 36 chars
No. No gain at all. The manual explicitly states:


  Tip: There is no performance difference among these three types, apart
  from increased storage space when using the blank-padded type, and a
  few extra CPU cycles to check the length when storing into a
  length-constrained column. While character(n) has performance
  advantages in some other database systems, there is no such advantage
  in PostgreSQL; in fact character(n) is usually the slowest of the
  three because of its additional storage costs. In most situations text
  or character varying should be used instead.


Bold emphasis mine.

char(n) is a largely outdated, useless type. Stick with varchar(n). Without need to enforce a maximum length, varchar or text are a tiny bit faster. (You won't be able to measure a difference.)

If all strings are exactly 36 characters in length, there is no storage saving either way, not even a minuscule one. Both have exactly the same size on disk and in RAM. You can test with pg_column_size() (on an expression and on a table column).

And if all strings must have 36 characters, rather make it text with a CHECK (length(col) = 36) constraint enforcing exact length, not varchar(36) only enforcing max. length.

Related:


Any downsides of using data type “text” for storing strings?


You didn't ask for other options, but I'll mention two:


COLLATION - unless you are running your DB with the "C" collation. Collation is often overlooked and possibly expensive. Since your strings don't seem to be meaningful in a natural language, there is probably no point in following COLLATION rules. Related:


How do I efficiently get &quot;the most recent corresponding row&quot;?
EXECUTE within function not using index?


Extensive benchmark comparing (among other) the effect of COLLATE "C" on performance:


Slow query ordering by a column in a joined table

UUID, obviously. Your string suspiciously looks like a UUID (32 hex digits plus 4 delimiters). It would be much more efficient to store these as actual uuid data type, which is faster in multiple ways and only occupies 16 bytes - as opposed to 37 bytes in RAM for either char(36) or varchar(36) (stored without delimiters, just the 32 defining char), or 33 bytes on disk. But alignment padding would result in 40 bytes either way in many cases.) COLLATION would be irrelevant for the uuid data type, too.

SELECT '922475bb-ad93-43ee-9487-d2671b886479'::uuid


This may be helpful (last chapters):


Convert hex in text representation to decimal number


See also:


What is the overhead for varchar(n)?
What is the optimal data type for an MD5 field?