RFR: 8342460: Remove calls to doPrivileged in javafx.web [v2]

[Andy Goryachev]

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

Andy Goryachev has updated the pull request incrementally with one additional commit since the last revision:

  review comments

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Changes:
  - all: https://git.openjdk.org/jfx/pull/1620/files
  - new: https://git.openjdk.org/jfx/pull/1620/files/ee1a9bfe..1c1e8eab

Webrevs:
 - full: https://webrevs.openjdk.org/?repo=jfx&pr=1620&range=01
 - incr: https://webrevs.openjdk.org/?repo=jfx&pr=1620&range=00-01

  Stats: 8 lines in 2 files changed: 7 ins; 0 del; 1 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