Is it safe to operate an HID lamp in a fixture that the outer envelope comes in contact with the metal reflector? Will the lamp explode?

Determine 'HID lamp'. There are thousands of types, some even expect to have an external support.

Generally, it is not advisable to have metal parts to touch hot glass. External bulb may crack because of thermal stress or because of the fact that hot glass may become somewhat conductive, and so, be damaged by electrolysis. The lamp is not at risk of explosion, though.

Beside the thermal stress, the somewhat hard surface of the reflector may also cause glass cracks (and those  may trigger the shattering) when the whole system is exposed to some vibrations. And these vibrations may be just the ballast humming in the fixture.

So unless it is a part really explicitly designed to be in contact with the lamp, I would not consider it safe for the lamp at all.

Now the question remains, whether this may really lead to lamp explosion.
Because we are talking about an outer bulb, which uses to have either vacuum inside, or max the same pressure as the atmosphere, I don't think an explosion is of any immediate risk. The outer bulb may shatter so send hot glass shards down, but nothing really violent.
However with some lamps the cracked outer may cause the inner arctube to get stresses over time (moly foil seals oxidizing and expanding within the seals) and lead to compromised arctube. And because the arctube uses to be operating under high pressure on many lamps, it may explode as a result. But this will take some time after the outer gives way, in the meantime the out of whack thermal balance (because the outer failure) will likely cause performance degradation of the lamp (color shifts,...) immediately when the outer fails, so gives quite some time to get detected. Plus most likely the arctube will fail during some runup, so when there is not yet that much pressure in it, so not in that violent way.

Definitely I won't expect the eventual arctube explosion to be any more violent the fixture (or the arctube explosion containment structure within the lamp itself if open rated) is supposed to handle in the first place.

Determine 'HID lamp'. There are thousands of types, some even expect to have an external support.

Generally, it is not advisable to have metal parts to touch hot glass. External bulb may crack because of thermal stress or because of the fact that hot glass may become somewhat conductive, and so, be damaged by electrolysis. The lamp is not at risk of explosion, though.

I was mainly referring to quartz metal halide and mercury vapor. The reason why I am asking was I was designing a downward remotely-ballasted light. But I was concerned about the neck of the bulb coming in contact with the aluminum bell reflector. And the lamp types I was planning to use were 175w metal halide or 175w mercury vapor. Is it bad if the lamp slightly touches the reflector. I have tried it with an EOL lamp and the reflector got hot. This fixture would only be used indoors with little temperature change.

In this case, probably depends on how much you value your lamp and if you will regret if you eventually destroy it. Are you able to move the lampholder slightly to avoid contact?

I suppose with minor adjustments.

Mainly with the aluminum and related alloys do not forget although the metal itself is rather soft, the aluminum oxide, which will always form on its surface, is one of the hardest materials on Earth, so pretty potent to dig into practically any glass when rubbing on it.

With your case I would consider opening up the hole in the reflector around the bulb neck, so you really make sure it wouldn't touch at all.
Because if it does, the forces involved could become pretty high - there I wouldn't expect either part "wanting" to get pushed away.

The packaging for my GE 750W PS52 incandescent lamp in my collection does give a specific warning about risks involved with metal contacting glass while the lamp is in operation.

I learned that a hard glass lamps like most any HID with goliath base will not cause any problems but lamps with soft glass like most incandescent lamps will fail almost certainly.

What about a LPS lamp being held (quite tightly) by a metal lamp support and spring?

LPS lamps have (obviously) very low thermal load, so thermal stress and electrolysis are not a problem.

the 1000W MH light towers we have at work have a metal wire support for the end of the lamp / they are BT style and it is a ring that the tube part opposite the screw cap and on some of the lamps there are grooves where the wire has worn the glass

But there the metal wire support is explicitly designed for the task, so the designers made sure it is not damaging the bulb (material selection, shape, flexibility, positioning, forces,...).
Usually reflector sheets are not controlled that well, so normally the lantern designs I've seen that have some ties between the lamp and reflectors, had dedicated support/spacers/insert structures between, so the lamp never touched the reflector directly. Of course, unless the lamp has an explicit feature designed to provide such interface (like the positioning collars on automotive headlight or some projector bulbs)