¿Solución en mysql para índice parcial o índice filtrado?

Los índices filtrados se pueden emular con índices de funciones y CASE expresión (MySQL 8.0.13 y posteriores):

CREATE TABLE t(id INT PRIMARY KEY, myColumn VARCHAR(100));

-- NULL are not taken into account with `UNIQUE` indexes   
CREATE UNIQUE INDEX myIndex ON t((CASE WHEN myColumn <> 'myText' THEN myColumn END));


-- inserting excluded value twice
INSERT INTO t(id, myColumn) VALUES(1, 'myText'), (2, 'myText');

-- trying to insert different value than excluded twice
INSERT INTO t(id, myColumn) VALUES(3, 'aaaaa');

INSERT INTO t(id, myColumn) VALUES(4, 'aaaaa');
-- Duplicate entry 'aaaaa' for key 'myIndex'

SELECT * FROM t;

db<>demostración de violín

Salida:

+-----+----------+
| id  | myColumn |
+-----+----------+
|  1  | myText   |
|  2  | myText   |
|  3  | aaaaa    |
+-----+----------+