list = {1, 4, 1, 2, 3, 5};
nonopt = {1, 3};

This gives a sorted output:

Complement[list, nonopt]

{2, 4, 5}

To preserve the order, this is a simple method.

DeleteCases[list, Alternatives @@ nonopt]

{4, 2, 5}

list = {1, 4, 1, 2, 3, 5};
nonopt = {1, 3};

This gives a sorted output:

Complement[list, nonopt]

{2, 4, 5}

To preserve the order, this is a simple method.

DeleteCases[list, Alternatives @@ nonopt]

{4, 2, 5}

Edit

For list with lists, matching on the first element:

list = {{1, a}, {4, d}, {1, x}, {2, b}, {3, c}, {2, y}, {5, e}};
nonopt = {1, 3};

DeleteCases[list, {Alternatives @@ nonopt, __}]

{{4, d}, {2, b}, {2, y}, {5, e}}

list = {1, 4, 1, 2, 3, 5};
nonopt = {1, 3};

This gives a sorted output:

Complement[list, nonopt]

{2, 4, 5}

To preserve the order, this is a simple method.

DeleteCases[list, Alternatives @@ nonopt]

{4, 2, 5}

list = {1, 4, 1, 2, 3, 5};
nonopt = {1, 3};

This gives a sorted output:

Complement[list, nonopt]

{2, 4, 5}

To preserve the order, this is a simple method.

DeleteCases[list, Alternatives @@ nonopt]

{4, 2, 5}