minecraft-java-edition
So I just found a stronghold and located the End Portal. I tried lighting up the area to get rid of the silverfish that come from the spawner, but I found out trough the Minecraft Wiki that when there's a spawner they can spawn at any light level.
Since I don't want to destroy the spawner, is there any way I can disable it? I know I can fill the room with blocks, but then access to the portal would get quite a bit complicated.
The conditions shown in your screenshot should be able to spawn pigs, assuming it's a pig spawner. I did a rough recreation of your setup in my world.
Even in the dark, pigs were spawning, and within seconds of placing the spawner, so it's not as if you aren't waiting long enough. (Yes, the pigs also spawned when I surrounded the spawner with Glowstone). Because of this, I have a feeling that the spawner in your image isn't actually a pig spawner; it's likely a zombie spawner, or some other hostile mob. This is especially likely if you found the spawner and it wasn't manually placed by anyone, since there wouldn't be any natural pig spawners around.
Like Kevin Reid said, you could test this by making the room dark and seeing if any hostile mobs spawn. If you have admin privileges (and don't feel like this is cheating in some sort of way), you could use /give 52 1 to give yourself an actual pig spawner, place it in the room, and see if that one spawns pigs, just to verify if this is an odd SMP glitch that is only happening for you.
There is a safe radius around the player where creatures can not spawn. Normally (depending on how big of a 'trap' you have built) the player's radius includes a dungeon spawning trap. The Dungeon Spawner is unique in that it ignores this normal requirement for spawning, which is why they keep appearing in front of you.
So, if your no-spawn radius includes the dungeon then you are ok. Also of note is that dungeon spawners will spawn creatures in mid-air and above water, normal creatures can not do this because of the spawning rules. Again, depending on the design of your trap it should be inherently safe.
However if wherever you are standing can be reached by just walking or 1 block jumps or multi-block drops, be aware that something can spawn outside of your safety radius and eventually find its way to you. I suggest only going AFK if you are completely sealed off :)
Best Answer
They actually stop spawning at light level 12 or higher, so surrounding the area with glowstone or redstone lamps should work.
Etho, a relatively famous YouTuber who specializes in exotic mob farms, has been working on a silverfish farm for a while: he went over how to disable a silverfish spawner using only light in episode 155 of Etho Plays Minecraft:
He had the same scenario you have: he wanted to keep the portal accessible but disable the spawner. He goes into possible caveats and problems you might run into, but he was able to completely disable the spawner by adding redstone lamps across the top of the spawning area.