type
  TCharSet = set of Char;

function IsStrValid(const Value: string; const Chars: TCharSet): Boolean;
var
  I: Integer;
begin
  Result := False;
  for I := 1 to Length(Value) do
    if not (Value[I] in Chars) then
      Exit;
  Result := True;
end;

// or another version of the same could be...
function IsStrValid(const Value: string; const Chars: TCharSet): Boolean;
var
  I: Integer;
begin
  Result := True;
  for I := 1 to Length(Value) do
    if not (Value[I] in Chars) then
    begin
      Result := False;
      Exit;
    end;
end;

var
  S: string;
const
  Allowed = ['A'..'Z', 'a'..'z', '0'..'9', '_'];
begin
  S := 'This_is_my_string_0123456789';
  if IsStrValid(S, Allowed) then
    ShowMessage('Ok')
  else
    ShowMessage('string contains invalid symbols');
end;