Both Postgres and MySQL are great. In history, Postgres emphasized more on feature development instead of performance, while MySQL took the opposite approach. It depends on your engineering and operation requirements to choose which one to deploy. Most of OP's points, however, need to have further consideration, IMHO.

- "While replication is indeed very important, are users actually setting up replication each time with MySQL or is it to only have the option later?"

Replication is not an option. It is a must-have for any serious products, both in scaling and in operation.

- Windows functions: They are wonderful and I love them. But it is not an important factor at all.

- Flexible datatypes: True in certain scenarios. It allows to create certain types to map a business object with unusual requirements. Otherwise, the requirements have to be implemented in application logic. But data type of Array? IMHO, use of Array data type in relational database usually means there are some issues in data modeling and design. The performance is another issue. If you have to use array, consider NoSQL options.

- Functions. Although I am a database architect, I use database functions only for simple poking around. For any serious work, I prefer to write application code. It is easier to maintain, to test, and to extend. I don't want to have a big muddy ball. I prefer to have structured, well-decoupled application code.

- Custom Language. Same as above. Why not just write application code?

- Extensions: Geospatial is awesome. It is better than that in MySQL. But for many extensions, I prefer not to do the computation in database. Databases are usually the most expensive resources (in operation costs) and are usually the performance bottle neck. It would be better to have the computation in app servers. It is easier to scale and it is cheaper.

- Custom Functions: see above.

- Common Table Expressions: Recursive queries are awesome. I t is nice to have for ad-hoc data inspection, but I wouldn't encourage its usage in application code. The risk to use it wrong vs the benefits are high if used in application code.