I'm using these two versions, and the game will not run with both installed simultaneously.

noxesium-1.1.1
dynamiccrosshair-7.6.2+1.20.2-fabric

Error log:
A mod crashed on startup!
net.fabricmc.loader.impl.FormattedException: java.lang.RuntimeException: Could not execute entrypoint stage 'preLaunch' due to errors, provided by 'dynamiccrosshair'!
at net.fabricmc.loader.impl.FormattedException.ofLocalized(FormattedException.java:63)
at net.fabricmc.loader.impl.launch.knot.Knot.init(Knot.java:162)
at net.fabricmc.loader.impl.launch.knot.Knot.launch(Knot.java:68)
at net.fabricmc.loader.impl.launch.knot.KnotClient.main(KnotClient.java:23)
Caused by: java.lang.RuntimeException: Could not execute entrypoint stage 'preLaunch' due to errors, provided by 'dynamiccrosshair'!
at net.fabricmc.loader.impl.FabricLoaderImpl.lambda$invokeEntrypoints$2(FabricLoaderImpl.java:388)
at net.fabricmc.loader.impl.util.ExceptionUtil.gatherExceptions(ExceptionUtil.java:33)
at net.fabricmc.loader.impl.FabricLoaderImpl.invokeEntrypoints(FabricLoaderImpl.java:386)
at net.fabricmc.loader.impl.launch.knot.Knot.init(Knot.java:160)
... 2 more
Caused by: net.fabricmc.loader.api.EntrypointException: Exception while loading entries for entrypoint 'preLaunch' provided by 'dynamiccrosshair'
at net.fabricmc.loader.impl.entrypoint.EntrypointContainerImpl.getEntrypoint(EntrypointContainerImpl.java:56)
at net.fabricmc.loader.impl.FabricLoaderImpl.invokeEntrypoints(FabricLoaderImpl.java:384)
... 3 more
Caused by: java.lang.RuntimeException: Mixin transformation of com.llamalad7.mixinextras.MixinExtrasBootstrap failed
at net.fabricmc.loader.impl.launch.knot.KnotClassDelegate.getPostMixinClassByteArray(KnotClassDelegate.java:427)
at net.fabricmc.loader.impl.launch.knot.KnotClassDelegate.tryLoadClass(KnotClassDelegate.java:323)
at net.fabricmc.loader.impl.launch.knot.KnotClassDelegate.loadClass(KnotClassDelegate.java:218)
at net.fabricmc.loader.impl.launch.knot.KnotClassLoader.loadClass(KnotClassLoader.java:119)
at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:525)
at java.base/java.lang.Class.forName0(Native Method)
at java.base/java.lang.Class.forName(Class.java:467)
at net.fabricmc.loader.impl.util.DefaultLanguageAdapter.create(DefaultLanguageAdapter.java:50)
at net.fabricmc.loader.impl.entrypoint.EntrypointStorage$NewEntry.getOrCreate(EntrypointStorage.java:117)
at net.fabricmc.loader.impl.entrypoint.EntrypointContainerImpl.getEntrypoint(EntrypointContainerImpl.java:53)
... 4 more
Caused by: org.spongepowered.asm.mixin.throwables.MixinApplyError: Mixin [noxesium.mixins.json:model.DyeableLeatherItemMixin from mod noxesium] from phase [DEFAULT] in config [noxesium.mixins.json] FAILED during PREPARE
at org.spongepowered.asm.mixin.transformer.MixinProcessor.handleMixinError(MixinProcessor.java:638)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.handleMixinPrepareError(MixinProcessor.java:585)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.prepareConfigs(MixinProcessor.java:543)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.select(MixinProcessor.java:462)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.checkSelect(MixinProcessor.java:438)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.applyMixins(MixinProcessor.java:290)
at org.spongepowered.asm.mixin.transformer.MixinTransformer.transformClass(MixinTransformer.java:234)
at org.spongepowered.asm.mixin.transformer.MixinTransformer.transformClassBytes(MixinTransformer.java:202)
at net.fabricmc.loader.impl.launch.knot.KnotClassDelegate.getPostMixinClassByteArray(KnotClassDelegate.java:422)
... 13 more
Caused by: org.spongepowered.asm.mixin.transformer.throwables.MixinTargetAlreadyLoadedException: Critical problem: noxesium.mixins.json:model.DyeableLeatherItemMixin from mod noxesium target net.minecraft.class_1768 was loaded too early.
at org.spongepowered.asm.mixin.transformer.MixinInfo.readDeclaredTargets(MixinInfo.java:948)
at org.spongepowered.asm.mixin.transformer.MixinInfo.(MixinInfo.java:882)
at org.spongepowered.asm.mixin.transformer.MixinConfig.prepareMixins(MixinConfig.java:852)
at org.spongepowered.asm.mixin.transformer.MixinConfig.prepare(MixinConfig.java:781)
at org.spongepowered.asm.mixin.transformer.MixinProcessor.prepareConfigs(MixinProcessor.java:540)
... 19 more

This usually happens when a mixin plugin is misconfigured to load Minecraft classes too early. Considering this has been reported to happen with other mods in combination with Noxesium (Noxcrew/noxesium#45) it's likely Noxesium's fault.