It can mean both "sign" and "penis". Nobody ever claims that it always only means "penis", but it often does. Your conspiracy theories make you look silly.
गुदे तिस्रः। तथैकात्र करे दश।
उभयोः सप्त दातव्याः। मृदः शुद्धिमभीप्सता॥
"Once to the penis
, thrice to the anus, ten times to one hand, seven times to both hands, earth should be applied by one who desires cleanliness."
Sanskrit-English dictionary by Vaman Shivram Apte:
6 The sign of gender or sex.
7 Sex; गुणाः पूजास्थानं गुणिषु न चलिंगं न च वयः U. 4. 11.
8 The male organ
9 Gender (in gram.)
10 The genital organ
of Śiva worshipped in the form of a Phallus
English-Sanskrit dictionary by Vaman Shivram Apte:
, s. लिंगं
, उपस्थः, शिश्नः, मेढ्रः, मेहनं, शेफस्
Sanskrit dictionary by Jibananda Vidyasagara Bhattacharya:
3. A sign of sex, the penis
4. The phallus
, or ŚIVA under that emblem.
None of these people are Muslims, म्लेच्छ॑s, or zoomers.
The शिवलिङ्ग is very clearly a phallic symbol and many of the earliest archeological attestations like picrel are even more clearly phallic. The fact that it's a penis isn't up to individual interpretation—only what ought to be done with that information.