RFR: 8342460: Remove calls to doPrivileged in javafx.web

[Andy Goryachev]

Removes `doPrivileged` calls in the javafx.web module, excluding the code in `{android,ios}`.

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Commit messages:
 - web

Changes: https://git.openjdk.org/jfx/pull/1620/files
  Webrev: https://webrevs.openjdk.org/?repo=jfx&pr=1620&range=00
  Issue: https://bugs.openjdk.org/browse/JDK-8342460
  Stats: 330 lines in 17 files changed: 12 ins; 218 del; 100 mod
  Patch: https://git.openjdk.org/jfx/pull/1620.diff
  Fetch: git fetch https://git.openjdk.org/jfx.git pull/1620/head:pull/1620

PR: https://git.openjdk.org/jfx/pull/1620