Having a Measure be effected by a Filter

First, is this import mode? If so, then split your food column out and unpivot the resulting columns.

Second, I do not understand why your filter and slicers should not impact your measures. As long as they are reducing the rows within 'MyTable', then the measure should be affected. 

Third, I really wouldn't use SELECTEDVALUE in that way but that's just me, I use MAX.

Hi andyismilesaway 

I prepared the table in Query Editor with the following steps:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WciwoyEnVUXBOLCrKL1HSUfJKzCtNLKoEsnzy81Ly85RidaKVAlITi5DU+CYWJWcAaaeizOKS/BywErA5QDHHgqLMHOy6izNSy3UUXNPTi4HyLqnJqblJqUUgYzKLcjPz0jMSc5ViYwE=", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type text) meta [Serialized.Text = true]) in type table [FavoriteFood = _t, DateofRespondant = _t, CityOfRespondant = _t]),
    splitColumn = Table.SplitColumn(Source, "FavoriteFood", Splitter.SplitTextByDelimiter(", ", QuoteStyle.Csv), {"FavoriteFood.1", "FavoriteFood.2", "FavoriteFood.3"}),
    unpivotFoods = Table.UnpivotOtherColumns(splitColumn, {"DateofRespondant", "CityOfRespondant"}, "Attribute", "Value"),
    remAttribute = Table.RemoveColumns(unpivotFoods,{"Attribute"}),
    renFavFood = Table.RenameColumns(remAttribute,{{"Value", "FavoriteFood"}})
in
    renFavFood

Paste into a blank query using Advanced Editor to follow my steps.

Then I created a number of measures for each fruit as follows:

_countApple = 
CALCULATE(
    COUNT(eTable[FavoriteFood]),
    eTable[FavoriteFood] = "Apple"
) +0

This gives me the following results and can be filtered by Date/City fine:

Pete