Much depends on how you translate the present middle imperative verb ἅπτου. Robertson's interpretation is "stop clinging" because "don't touch" would be aorist middle imperative. Thus, a component necessary for answering the question is another question, Is Roberson's interpretation valid?
The tendency is to translate ἅπτω as cling.
II. Med. to fasten oneself to, cling to, hang on by, lay hold of, grasp, touch, c. gen., ἅψασθαι γούνων, as a suppliant,… -- Liddell, H. G. (1996). A lexicon: Abridged from Liddell and Scott’s Greek-English lexicon (p. 112). Oak Harbor, WA: Logos Research Systems, Inc.
However, a Hebrew word meaning cling relates to friendship.
In addition to these words and expressions, a variety of verbal forms and idioms are associated with the friend, and these provide us with additional insight into biblical presuppositions about friendship: dbq, “to cling (to),” an idiom of loyalty used of the friend in Prov 18:24 and Ruth 1:14;… -- Olyan, S. M. (2017). Friendship in the Hebrew Bible. (J. J. Collins, Ed.) (pp. 4). New Haven; London: Yale University Press.
“there is a friend who clings more closely than a brother,” Prov 18:24… -- Olyan, S. M. (2017). Friendship in the Hebrew Bible. (J. J. Collins, Ed.) (p. 5). New Haven; London: Yale University Press.
Other usages of the verb “to cling to” that have a clear physical connotation (e.g., Ruth 2:8, 21, 23) suggest that a sense of physical proximity as well as loyalty may be implied in a passage such as Prov 18:24.-- Olyan, S. M. (2017). Friendship in the Hebrew Bible. (J. J. Collins, Ed.) (p. 17). New Haven; London: Yale University Press.
“clinging” among family members is likely both behavioral (remaining in close proximity) and emotional but not sexual. Olyan, S. M. (2017). Friendship in the Hebrew Bible. (J. J. Collins, Ed.) (p. 17). New Haven; London: Yale University Press.
A particular example of clinging is how Ruth stayed with Naomi, when she had no obligation to do so. Mary fit this friendship example of clinging. She listened to Jesus’ teaching to the complaint of Martha. Mary’s hurt because Jesus allowed Lazarus to die was beyond conversation. Mary was at the crucifixion. She was at the tomb, even when no one else was. What was the nature of Jesus’ statement to stop clinging?
Touch me not (μη μου ἁπτου [mē mou haptou]). Present middle imperative in prohibition with genitive case, meaning “cease clinging to me” rather than “Do not touch me.” -- Robertson, A. T. (1933). Word Pictures in the New Testament (John 20:17). Nashville, TN: Broadman Press.
However you interpret μή μου ἅπτου, γὰρ is important in οὔπω γὰρ ἀναβέβηκα πρὸς τὸν πατέρα (in John 20:17, NA28). With the interpretation of cling it seems Jesus us saying, "Mary, don't emotionally and mentally expect me down here on Earth because I'm still here. Soon I will return to the Father."
The Peshitta has ܠܴܐ ܬܷ݁ܬ݂ܩܰܪܒ݂ܺܝܢ, which has the idea of approach. The Greek makes sense with this idea, "Stop approaching me."
Use in LXX: