This is because they share the same transclusion variable, you can prevent that like this:
<$let transclusion="taglist1">
...tagpicker here..
</$let>
<$let transclusion="taglist2">
...tagpicker here..
</$let>
Top achieve what you have in mind I think my improved tagpicker macro can help you :Demos — Q&A and tools for tiddlywiki , it can filter the list of tag picked.
I included it in the complete solution bellow:
\import [[$:/core/ui/EditTemplate/tags]]
\define tag-button(classes)
	<$let button-classes='tc-btn-invisible $classes$' currentTiddler=<<tag>>>
		{{||$:/core/ui/TagPickerTagTemplate}}
	</$let>
\end
\define tagsAutoComplete()
<$list filter=<<tagsAutoCompleteFilter>> emptyMessage=<<tagsAutoCompleteEmptyMessage>> variable="listItem">
	<$list filter=<<tagsFilter>> variable="tag">
		<$list
			filter="[<tag>addsuffix<suffix>] -[<tagSelectionState>get[text]]"
			emptyMessage=<<tag-button 'tc-tag-button-selected'>>
			variable="ignore"
		>
			<<tag-button>>
		</$list>
	</$list>
</$list>
\end
\define tag-picker-inner(actions,tagField:"tags")
\whitespace trim
<$let 
	newTagNameInputTiddlerQualified=<<qualify "$:/temp/NewTagName/input">> 
	newTagNameSelectionTiddlerQualified=<<qualify "$:/temp/NewTagName/selected-item">> 
	fallbackTarget={{$(palette)$##tag-background}}
	colourA={{$(palette)$##foreground}}
	colourB={{$(palette)$##background}}
	storeTitle={{{ [<newTagNameInputTiddler>!match[]] ~[<newTagNameInputTiddlerQualified>] }}} 
	tagSelectionState={{{ [<newTagNameSelectionTiddler>!match[]] ~[<newTagNameSelectionTiddlerQualified>] }}}
	refreshTitle=<<qualify "$:/temp/NewTagName/refresh">>
	nonSystemTagsFilter="[tags[]] $(tagListFilter)$ +[!is[system]] -[<storyTiddler>tags[]] :filter[search:title<userInput>]+[sort[]]"
	systemTagsFilter="[tags[]] $(tagListFilter)$ +[is[system]] -[<storyTiddler>tags[]] :filter[search:title<userInput>]+[sort[]]"
	displayTagsPopup="[all[tiddlers]subfilter<systemTagsFilter>][all[tiddlers]subfilter<nonSystemTagsFilter>] +[limit[1]]"
>
<div class="tc-edit-add-tag">
	<div>
		<span class="tc-add-tag-name tc-small-gap-right">
			<$macrocall $name="keyboard-driven-input"
				tiddler=<<newTagNameTiddler>>
				storeTitle=<<storeTitle>>
				refreshTitle=<<refreshTitle>>
				selectionStateTitle=<<tagSelectionState>>
				inputAcceptActions="<$macrocall $name='add-tag-actions'
				actions=<<__actions__>>
				tagField=<<__tagField__>>/>"
				inputCancelActions=<<clear-tags-actions>>
				tag="input"
				placeholder={{$:/language/EditTemplate/Tags/Add/Placeholder}}
				focus={{{ [{$:/config/AutoFocus}match[tags]then[true]] ~[[false]] }}}
				focusPopup=<<qualify "$:/state/popup/tags-auto-complete">>
				class="tc-edit-texteditor tc-popup-handle"
				tabindex=<<tabIndex>> 
				filterMinLength={{$:/config/Tags/MinLength}} 
				cancelPopups=<<cancelPopups>>
				configTiddlerFilter="[[$:/core/macros/tag-picker]]"
			/>
		</span>
		<$button
			popup=<<qualify "$:/state/popup/tags-auto-complete">>
			class="tc-btn-invisible tc-btn-dropdown"
			tooltip={{$:/language/EditTemplate/Tags/Dropdown/Hint}}
			aria-label={{$:/language/EditTemplate/Tags/Dropdown/Caption}}
		>
			{{$:/core/images/down-arrow}}
		</$button>
		<$reveal state=<<storeTitle>> type="nomatch" text="">
			<$button
				class="tc-btn-invisible tc-small-gap tc-btn-dropdown"
				tooltip={{$:/language/EditTemplate/Tags/ClearInput/Hint}}
				aria-label={{$:/language/EditTemplate/Tags/ClearInput/Caption}}
				actions=<<delete-tag-state-tiddlers>>
			>
				{{$:/core/images/close-button}}
			</$button>
		</$reveal>
		<span class="tc-add-tag-button tc-small-gap-left">
			<$let tag={{{ [<newTagNameTiddler>get[text]] }}} currentTiddlerCSSEscaped={{{ [<saveTiddler>escapecss[]] }}}>
				<$button set=<<newTagNameTiddler>> setTo="">
					<$action-listops $tiddler=<<saveTiddler>> $field=<<__tagField__>> $subfilter="[<tag>trim[]]"/>
					$actions$
					<<delete-tag-state-tiddlers>>
					<$action-sendmessage $message="tm-focus-selector" $param=<<get-tagpicker-focus-selector>>/>
					{{$:/language/EditTemplate/Tags/Add/Button}}
				</$button>
			</$let>
		</span>
	</div>
	<$reveal
		class="tc-block-dropdown tc-block-tags-dropdown tc-block-dropdown-wrapper"
		default={{{ [subfilter<displayTagsPopup>then[]else[hide]] }}}
		state=<<qualify "$:/state/popup/tags-auto-complete">>
		tag={{{ [subfilter<displayTagsPopup>then[div]else[template]] }}}
		text=""
		type="nomatch"
	>
		<$let
			actions=<<__actions__>> 
			currentTiddler=<<tag>>
			tagField=<<__tagField__>>
			userInput={{{ [<storeTitle>get[text]] }}}
			tagsAutoCompleteFilter="[<userInput>minlength{$:/config/Tags/MinLength}limit[1]]"
			tagsAutoCompleteEmptyMessage="<div class='tc-search-results'>{{$:/language/Search/Search/TooShort}}</div>"
		>
			<$let tagsFilter=<<nonSystemTagsFilter>> suffix="-primaryList"><<tagsAutoComplete>></$let>
			<hr>
			<$let tagsFilter=<<systemTagsFilter>> suffix="-secondaryList"><<tagsAutoComplete>></$let>
		</$let>
	</$reveal>
</div>
</$let>
\end
\define pick-tag(tagField, tagListFilter)
<$messagecatcher $tm-focus-selector>
<$let
saveTiddler=<<currentTiddler>>
transclusion=<<__tagField__>>
tagListFilter=<<__tagListFilter__>>
>
<$macrocall $name="edit-tags-template" tagField=<<__tagField__>>/>
</$let>
</$messagecatcher>
\end
Include: <$macrocall $name="pick-tag" tagField="include" tagListFilter="-[<saveTiddler>get[exclude]enlist-input[]] -[<saveTiddler>get[include]enlist-input[]]"/>
Exclude: <$macrocall $name="pick-tag" tagField="exclude" tagListFilter="+[<saveTiddler>get[include]enlist-input[]tagging[]] -[<saveTiddler>get[exclude]enlist-input[]tagging[]] +[tags[]] -[<saveTiddler>get[include]enlist-input[]] "/>
Matches:
<table class="tc-max-width">
<thead><th>Tiddlers</th><th>Tags</th></thead>
<tbody>
<$list filter="[<storyTiddler>get[include]enlist-input[]tagging[]] :except[<storyTiddler>get[exclude]enlist-input[]tagging[]]-[is[system]]" variable="transclusion">
<tr>
<td><$link to=<<transclusion>> /></td><td><$list filter="[<transclusion>tags[]]"><<tag>></$list></td>
</tr>
</$list>
<tbody>
Here I use a </$messagecatcher> to prevent the focus to switch between the two tagpicker, but there is probably a better and cleaner way to do this.
Demo:  Demos — Q&A and tools for tiddlywiki
You can easily add more filters in the tagListFilter attribute or in the list widget.