Would comparison of strings to a postgres 'text' type column for equality be a performance bottleneck?
Yes, text is (roughly) equivalent to varchar(max)

Comparing text values is not less efficient than comparing varchar values in Postgres as under the hood they are absolutely identical. So the efficiency of the comparison is related to the length of the values. I don't expect that to be any slower than your current implementation using varchar(max) in SQL Server. 

If you want to enforce uniqueness on a column, create a unique index on it. Then you can use insert ... on conflict do nothing to efficiently insert new values and at the same time validating that they are unique.

However: there is a technical limit on how long an index entry is allowed to be which is roughly 2700 byte. You didn't mention how long your values are, but the index might not work for you then. 

Consider also this answer https://dba.stackexchange.com/a/69164